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Preview: Math 816 (2007)

Math 816 (2007)





Updated: 2014-10-05T01:56:13.623-05:00

 



Kiahna's Scribe Post

2008-05-14T16:44:37.174-05:00

Algebra Problem Solving!!
1. Mr. Enigma said, five less then one fourth of my age is 12 how old is Mr. Enigma?
Mr Enigma is 68 years old. Let x=his age
we are going to make x=1 becasue you can do that. they answer is

x/4-5=12
+5 +5
(4)x/4 17(4)
x= 68

2. Suppose you have $40 and you earn $7 per hour. How many hours must you work untill you have $131?
You would have to 28 work hours
7x+40=131
-40 -40
7x/7 91/7
x=28

3. Valley video charges a $15 annual fee plus $3 per movie for rentals. Last year, Jennifer spent $99 at the store. How many movies did she rent?
She rented 99 movies?
3x+15=99
-15 -15
3x/3 84/3
x=28

5.Suppose you are salesperson for Quark Compuer Company. Each month you earn $500 plus one sixth of your sales. What amount must you sell this month to earn $3000?
The amount he would have to sell was 15000.
x/6+500=3000
-500 -500
(6) x/6 2,500(6)
x= 15,000
6. For lunch Dregg had a hamburger and potato chips. The hamburger had 325 calories and each chip had 12 calories. If the meal had 541 calories, how many chips did Dregg eat?
He ate 18 chips.
12x+325=541
-325 325
12x/12 216/12
x=18




Robby's Scribe

2008-05-13T20:27:12.333-05:00

Today in class, we got this algebra work sheet. So, I'll do some of the questions on the number-answer sheet, not geometry side.Question 1:The second of two numbers is 4 times the first. Their sum is 50. Find the numbers.Ok, so, to answer this question, we have to find out which is the variable and have it equal 50. It also says "sum", so there is going to be addition in this question.To find the variable, you have to read the sentence and find out what part of the question isn't told. But first, write the simple-sentence answer, which is just the answer in a sentence. You write this out first, then come back to it once u find the numbers. 10 40The numbers are ____ and ____. (You can also write this at the end of the equation, which is what I'm going to do just to make it make more sense.)"The second of two numbers"This means that, in the equation, the second number will NOT be the variable, because if u read on..."is 4 times the first". This means it will be 4x, not just x, which is what we need.So the first number will be x.Remember, you have to have the "Let X = blahblah" somewhere in that equation, or u lose marks.Moving on, 4x would be on the right side of the + sign, because it is the second number. The first number is x.So the equation would look like this:Let x = First numberx + 4x = 50 (what we have so far)5x = 50 (combined like terms)-- ---5 5x = 10The answer to this question would be 10, 40.SUBSTITUTE TO CHECK (this is to make sure you have the right answer)x + 4x = 50 (must write formula)10 + 4(10) = 5010 + 40 = 5050 = 50x = 104x = 40 (this is very important too, before you write your answer into the sentence, you have to write out what the variable and term stand for in numbers, like above. Now you see why its easier to write the sentence at the bottom)If the answer on the left side equals the right side (50 = 50), that means the number works.Question 2:(I will now be writing all the answers out with some info in brackets, if you don't get it, go back to Question 1: and read on how to get it.)The larger of two numbers is 12 more than the smaller. Their sum is 84. Find the numbers."Larger of two numbers is 12 more than smaller"The two other numbers would equal x, because nothing is told about them.Let x = Smaller Number 1, Smaller number 2.x + 12 + x + x = 843x + 12 = 84 (combined like terms) -12 -123x = 72-- ---3 3x = 24Substitute to Check:x + 12 + x + x = 843(24) + 12= 8472 + 12 = 8484 = 84x+12 = 36x = 24x = 24 36 24 24The numbers are ____, ____, and ____.The answer would be 36, 48 [because 36 is 24 + 12 and 48 is 24 + 24 (2 x 24)]Question 4:The second of two numbers is 5 more than twice the first. Their sum is 80. Find the numbers."second of two numbers"So the second number would be the term (number with the x or a or whatever letter next to it)and the first number would be the variable.Let x = First Number"5 more than twice the first"2x + 5"sum is 80"= 80Now put it al together...x + 2x + 5 = 803x + 5 = 80 - 5 -53x = 75-- ---3 3x = 25Substitute to Check:x + 2x + 5 = 803(25) + 5 = 8075 + 5 = 8080 = 802x+5 = 55x = 25 25 55The numbers are _____, and _____.25, 55.Question 6:Find two numbers whose sum is 92, if the first is 4 more than 7 times the second. Find the First number."Two numbers whose sum is 92, if the first is 4 more than 7 times the second"so the second number is x, because it doesn't mention anything about it.Let x = Second Number(7x + 4) + x = 92 (brackets there to make it look simpler)8x + 4 = 92 (combined like terms) - 4 -48x = 88-- --8 8x = 11Substitute to check:(7x + 4) + x = 928(11) + 4 = 9288 + 4 = 9292 = 92x = 117x + 4 = 81The first number is 11.Question 8:Together, a necklace and a bracelet cost $192. Find the price of each if the necklace costs 3 times as much as the bracelet."if the necklace costs 3 times as muc[...]



Romulo's Scribepost

2008-05-13T21:09:41.806-05:00

SCRIBE POSTSo today in math we first went over this math sheet we had for homework called 7.3 Solving Geometric Problems. This took up about 45 minutes of the class and for the rest of the class we had time to do some of our homework which I'm scribing today.Since no one has scribed anything about Algebra problem solving I'll post the 6 steps.1. Simple Sentence Answer2. Unit Values3. In A Geometry Question DRAW THE SHAPE4. Whatever You Know Nothing About Is The Variable5. Identify Your Variable6. The Other Unknown Relates To The VariableThose are the 6 steps for sucess.Here's an example on how you solve an Algerbra problem solving question.The question is "A farmer uses 54 metres of fencing to enclose a rectanguler field. If the width is two metres less than the length, find the dimensions of the field.1. Simple Sentence AnswerFor the simple sentence answer all you need is 3 words. Those 3 words areThe, are and whatever the question is asking you to find. So in this case your looking for the dimensions. So your simple sentence answer would beThe dimensions are _________ and _________2. Unit ValuesUnit values simply ask you to put whatever value you're working with in your simple sentence answer. So since we're working with metres you put "m" in your sentence. So it should now look likeThe dimensions are _________m and _________m3. In A Geometry Question DRAW THE SHAPEThis one pretty self explanitory4. Whatever You Know Nothing About Is The VariableFor this one your variable(x or n or whatever you want) is the thing you have no clue about. So your first need to figure out who the playaz are. So the playaz are length, width and the perimeter. We know already know that the perimeter is 54 metres so it can't be the variable. We also know that the width is 2 metres less than the length so that leaves us with length which we know nothing about. So length is the variable.length= variable5. Identify Your VariableI don't really understand this step but I think this is the one were we have to remember to put let x= length somewhere or we lose a half a mark. So addx= length6. The Other Unknown Relates To The VariableI dont really understand this one but I think it means if you have two unknowns they relate to the variable.After all 6 of those steps you can finally start doing your work.So all that was just an explanation on the steps. Now to get to the point of this scribepost. So the side I'm doing is the geometry side. The side that has the titleWhat's the Quickest Way for an Ant to Go From the Ground to the Tree TrunkQuestions1. The length of a rectangle is 3 times the width. The perimeter is 96 cm. Find the width and length.2. The length of a rectangle us 5m greater than the width. The perimeter is 150m. Find the width and length[...]



Jonah's Scribe

2008-05-07T22:46:05.779-05:00

Today in class...

We went over the homework to see if we had any questions about it and solved it together. Then we learned how to solve a 2 Step Equation. Here are the steps:
1. Isolate the variable
2. cancel the constant (integer) using its composite to make zero pairs.
3. Balance
3a. cancel variable to (1.)
4. Substitute to check.

Here is an example:

(image)
But, we didn't just learn how to show in that way. We also were shown how to show it by using Algetiles. Here is the example used in class:

(image) That is how we use Algetiles to show 2 Step Equations! That is all we did in class. don't forget to do the homework we got.







Jordan's Scribe Post

2008-05-06T19:25:50.765-05:00

(image)




First, we started with 3 patterns:(image) Then we had to find the next 2 patterns, which were:
(image) Then we had to make a T-Chart for the patterns we found...
(image) the numbers in the "y" row start at 1 and go up by 2 each time..
the numbers in the "x" row start at 0 and go up by 1 each time..
to get "y," you have to multiply "x" by 2, then add 1
Algebraic expression: y = 2n+1
(image) We started off with 3 different patterns this time... The 5 pictures looked like this:
(btw, the vertical lines through the strings are the cuts)
(image) Followed by the T-Chart:
(image) We found that the "y" row started @ 1 then increased by 3 each time
We found that the "x" row started @ 0 then increased by 1 each time
You have to multiply "x" by 3 then add 1 to get "y"
Algebraic Expression: y = (3n)+1
THE END.















Marina's 2nd Scribe Post

2008-05-06T08:04:53.905-05:00

My Scribe

Okay today in class, I volunteered to do a scribe post. I made a little slideshow on voicethread, i dont really know if i did it right so yeah...
P.s. I did this all on piant,so it ,might be messy.. didnt take me very long.

(embed) (image)

-marina☺☻○



Robby's Scribe

2008-05-05T18:40:45.377-05:00

Collecting Like TermsLike terms are Terms that have the same Variables next to them. Variables are letters that stand for unknown or given numbers. Like terms are 2 or more terms that can be combined to simplify the equation. Lets look at an example:This right now is an algebraic math sentence. In algebra, you don't always have to find an answer to the question, that is, if you aren't told what the variable stands for. This is one of those occasions.In algebra, you don't use all the operators you would use for non-algebraic equations. Like, for example, times (x). Because times has a operator that looks like a variable, it gets confusing (Like so: Variable x X x = x ...no it's not what you were thinking). So they removed it (they being those math geniuses that invented algebra). Instead of writing 5 x (x+2), you remove the x and assume its multiplication. And when multiplying a number with a variable, you write them next to each other (5x). This becomes a Term.Back to the math sentence in blue above. An easy way when multiplying things in brackets and theres a variable in there is to multiply the outside number with the variable. So it would look something like this: Like I said before, when multiplying a number with a variable, you put the variable on the right side of the number and it becomes a term. So 5x means Five groups of variable x.The next part of the question is the +2. You would read this as positive two, because in algebra, you deal with integer numbers a lot. Now you have to multiply it with 5 now, because its still in the brackets, and if there's no operator between the brackets and number on the outside, you assume its multiplication.Now, we multiply the 5 with the 2. 5 x 2 = 10 (note, I used the x symbol for multiplying because we aren't multiplying the terms, and this equation won't go in the final answer, only the 10 will)The math sentence now looks like this:This is a proper algebraic sentence. The terms should always be on the left side, and the non-terms, or integers, on the right. Now to to show you how to write this question using algebra tiles. But first, look at the different kind of shapes used to represent the parts of a algebraic-math sentence.Now that we know what shapes I'll be using mean, on with the algebra-sentence. I'll simply show what the simplified answer to the algebra sentence near the middle of my scribe-post looks like with algebra tiles...=[...]



David's Scribepost

2008-05-02T06:11:25.339-05:00

Algebra Tiles Algebra tiles are ways of showing algebra. The big sqares are the variable (n, x) squared, the long rectangles are the variable, and the little squares are the integer or the constant, it's just the number. There are two sides to Algebra Tiles, a white side, and a colored side, the white side means its a positive number, the colored side means its a negative number. So if your question is 3n+6 and you wanted to draw it out using Algebra Tiles, then it would look like this...Theres something else that comes into effect when we do this, and its Zero Pairs. Zero pairs are when you have a positive and a negative, and they cancel eachother out. It's like you owe money if there's a negative, and the positvive is how much money you have. Thats just one good way to try and understand intergers.Afrer that we just did a bunch of questions and figured them out using algebra tiles, one of them would be 2n-6+4n-2+6-n. So how would you draw that out? Now if you can't tell where to start and which sign belongs to what, then try making the catapiller, start at the first number / opperation and circle to the next one.Now thats nice but we want to group them.We can get rid of some by finding zero pairs!and we're left with 5n-2And thats how you use Algebra tiles. We had homework too, 3 pages of it. ^ ^ On this one you only need to do up to question 18...^^Good luck finnishing! I'm sure there's going to be more work.[...]



Nathaniel's Scribe Post

2008-05-02T00:16:14.048-05:00

Patterns 2!!Mr. Jerema gave us two charts the other day. We had to make a chart and a ratio table, describe the patterns in each row, describe the relationship between the two columns, make an algebraic equation to show that relationship, then find out what the 20th, 35th, and 99th diagram would be.This is the first chart he gave us.We had to make that into a chart.. like soand into a ratio table..3. Describe the patterns found in each row.Well you can see that x, starts at 1 and goes up by 1, and y, starts at 1 and goes up by 2.4. Describe the relationship between the two columns.If you have the years over 10, and lets say you have 2. You would have to multiply it by two and subtract one to get y, since this works for all the years over 10.C. Write and algebraic equation to show this relationship.y=2x-1 x = years over 105. Predict what the 20th, 35th, and 99th diagram will look like.We use the algebraic expression here, and having 20, 35, and 99 the years over 10.note:re write the expression and fill it in.20th- 2x-1- 2(20)-1- 3935th- 2x-1- 2(35)-1- 6999th- 2x-1- 2(99)-1- 197Now back to number one since instead of drawing the next two patterns, he said to find out the number of repairs for 7 and 8 years over 10.7th- 2x-1- 2(7)-1- 138th- 2x-1- 2(8)-1- 15And were done the car repairs! Onto Harbecks Training.Then we had to make a chart, and a ratio table out of it..3. Describe the pattern found in each row.As you can see, x starts at one and increases by one each time, and y starts at 3, then adds 5, 7, 9 and adding so on by odd numbers.4. Describe the relationship between the two columns.If you have the number of weeks, to get the number of km's ran in total, you would have to multiply the number of weeks by itself, and subtract one to get the number of km's ran in total.c. Write an algebraic equation to show this relationship.y=x squared - 1 x=number of weeks5. Predict what the 20th, 35th, and 99th diagram will look like.20th- xsquared-1- 20squared-1- 39935th- xsquared-1- 35squared-1- 122599th- xsquared-1- 99squared-1- 9801Then back to number one to find out what the 7th and 8th diagram will look like.7th- xsquared-1- 7squared-1- 488th- xsquared-1- 8squared-1- 63and your done![...]



Angel's Scribe

2008-05-01T22:31:42.474-05:00

Algebra Test #1 For the first part of the test we had to write the following expressions in words..3x+8 : Three times a number and eight 7x+5x : Seven times a number and five times a number 5(x+8) : Five times the sum of a number and eight 8-3x : Eight decreased three times a numberFor the bottom of the first part of the test we had to write the following statements as algebraic expressions.. 5. 9 centimeters less than three fourts of length x : 3/4x-9 6. Seven decreased by four times a number : 7-4n7. 9 less than 3 times a number : 9-3x 8. four more than eight times a number : 8x+4For the second part of the test we had to make a t-chart, graph and figure out the algebraic equation for the following problem ..This is my T-chartThe patter : x = Figure number, Starting with one going up by one.y = Number of tiles, starting with four and adding three each time.Here is my Graph How to get the answer x=Figure numbery=Number of tilesThe algebraic equation is 3x+7 [...]



Vicky's Third Scribe

2008-05-01T21:33:29.786-05:00

Today in class, I volunteered to do a scribe post for this month on algebra test number 2.
This is what the Algebra Test 2 looks like.
Algebra Test 2
Write the following expressions in words.
1. 2x-9 = two times a number decreased by (less, reduce, take away, etc.) nine.
2. 10-4x = ten decreased by (reduce, and decreased ONLY) four times a number.
3. 5 (x-8) = a number less (decreased, take away, etc.) than eight times five.
4. 7(x+5) = a number plus (increased, and, sum of, etc.) five times seven

Write the following statements as algebraic expressions
5. 6 centimeters more than two thirds of lenth x = 2/3 n + 6cm
6. three times the sum of a number and two = 3 (n+2)
7. nine decreased by two times a number = 9-2n
8. four less than five times a number = 5n-4

The following graph shows the first four terms of a pattern.



A) Create a chart that shows the first 10 terms of the pattern.

B) Write the algebraic expression for the relationship between the hours spent walking and the number of kilometers walked.
4n - 1
y is km walked
x is hours
C) Using your algebraic expression, determine how far they could walk after 50 hours.
4n-1
4 x 50 huors - 1 = 199 km
Done!~ Teehee!~








Vicky's Bob

2008-04-26T22:17:11.541-05:00

What I Know About Rectangular Prisms


Rectangular Prism, also known as Cuboid (the shape), is a solid 3D (3-dimensional) object which has six faces, Top, Bottom, Left, Right, Front and Back. Each opposite faces of a rectangular prism are equal, for example Top is equal to Bottom, Left Side is equal to Right Side, and Front is equal to Back.

(image)

A Net is a disasemble box, or an open box. Its very usefull when you want to find the area of each faces.




(image)

This is an old voice thread that I have used on my second scribe post. Yes, I have finally changed it to public, sorry for the technical difficulties~. Teeehheeee.
(object) (embed) (image)
How to find the volume of a rectangular prism.

(object) (embed) (image)



emilyr's bob

2008-04-24T18:41:33.623-05:00

What I Know About Rectangular Prisms ;
A rectangular prism is a 3d object that has length, width and height.
(image)
When its flattened it is called a Net. A net is just how you look at the prism when you open it all up. The net helps you get the surface area.
(image)
l= length
h= height
w= width


To get the surface area you can find the area of all the parts (top, bottom, front, back, left side and r side) then add them all up. The easier way is to use formulas.
The formula for top and bottom is: LxWx2.
The formula for front and back is: LxHx2.
The formula for the two sides is: WxHx2.


After you find the area for those you add them all after. After you add them you have you're surface area. The surface area is usually cm² or something².

Another thing I learned was to get the volume. The volume for formula is LxWxH or BxH. The B stands for Base and the H stands for Height.

The volume is usually something³
For examples look at my scribe post






Angel's Scribe Post

2008-04-17T00:02:10.365-05:00

Cylinders and Circles
Today in class we learned about the circles and its radius, diametre, and circumferance. Later on during class we also learned how to find the area of a cylinder.
All about the radius and diameter : In class we were told that radius is the distance from the centre of the circle to the edge and you can get it by dividing the diameter because the diameter is double the distance of a radius going from one edge of the circle to the other. The formula to get the diameter : d=2r. meaning the diameter = 2x the radius.

The circumference : The circumference is the distance around a circle. You can get this by 2Pi r (2 x pi x r) pi 2r or pi x diameter.

Cylinder : In class we learned how to make a net of a cylinder.
>PLEASE DO NOT DRAW A PEN15<
also make sure that the circles are the same size.

(image) L = Circumference
W = Height

FORMULA
A = Pi R2 C = Pi D
A = 3.14 x 5cm2 C = 3.14 x ??cm
A = 3.14 x ??cm C = 3.14
A = ??cm2


Total surface Area : ??cm2+??cm2+??cm2 = ??cm2








Nathaniel's BOB

2008-04-15T23:29:26.200-05:00

What do I know about Rectangular Prisms?

I have learned about length, width and height of a rectangular prism.
(image) I have also learned that you can open it up to make it flat. It is called a net! Each side still is the length, width, and height.
l=length
h=height
w=width

(image)
To find the surface area you have to add up all the sides squared.
If you had a 2x2x3 prism, you would have to multiply..

LxHx2
LxWx2
HxWx2

LxHx2 is the front and back of the prism.
LxWx2 is the top and the bottom of the prism
HxWx2 is the left side and right side of the prism.

After you add it up you should have the surface area.
(image) To find the Volume of a rectangular prism, you can just do Length x Width x Height!
Volume is how many cubed (insert measurement here example cm) can fit inside the prism.

If the length = 2cm
width = 2cm
height = 3cm

You would do 2cm x 2cm x 3cm to get the volume
The volume would be 12cm cubed.



Ps: hooray 200th post!



Jonah's bob

2008-04-15T21:50:44.077-05:00

What I know and learned about rectangular prisms:We learned about getting the Surface Area and Volume of rectangular prisms. But the step we always do is making a Net.Surface Area:There is a lot of work to do before you can actually find out the surface area. You have to find out the area of each of the shapes. The top, front, and the left side. You only need to find out only one of each shape because each one has a pair. The right and left sides, the front and back, and the top and bottom.The formula for figuring out the top and bottom is LxW (length x width). Since you only need to find out one of each shape all you have to do is then multiply it by 2. So it would be lxwx2 to equal the answer with a exponent of 2 (squared). E.g 3cm x 2cm x 2 = 12 2 cm.The formula for figuring out the sides is HxW (height x width). Again, since you only need to find out only one side all you have to do is multiply it by 2. So then it would be hxwx2 to equal the answer with an exponent of 2 (squared). E.g 6cm x 2cm x 2 = 24 2 cm.The formula for figuring out the area for the front and back is HxL (height x length). Since you only have to find out one of the shapes all you have to do is multiply the first answer by 2. So then it would be hxlx2 to equal the answer with an exponent of 2 (squared). E.g 6cm x 3cm x 2 = 36 2 cm.Then you add all the numbers to together to get the total surface area. The exponent for surface area is always 2.Volume:Figuring out the volume for a rectangular prism is some what harder that find the surface area. But in some ways it is easier because you are only figuring out what is the number of the inside of the shape. There are two formulas of finding the volume.Area of the base x Width is one of the formulas. First you find out the measurement of the base. Then you multiply that by the width because that is how many base numbers you have. E.g Base number = 15 cm 2 and the width = 3 cm. So it would be 15 cm 2 x 3 cm= 45 cm 3.The second formula is LxHxW (length x height x width). You first find out the measurement of the length, width, and the height. Once you do then you multiply them all together. E.g L = 5 cmH = 10 cm W= 3cm. 5cm x 10 cm x 3 cm = 150 cm 3.The exponent for volume is always 3.[...]



Kierra's BOB

2008-04-15T20:15:07.018-05:00

Everything I Know About Rectangular Prisms:In class we learned how to find the surface area/ volume/ & net of squares and rectangular prisms. Net:A net is a picture of a 3 dimensional object flattened out so you are able to view all sides n one dimension.E.G:The yellow shaded parts in the picture reps. the sides of the rectangle. The black shaded parts represent the top and bottom of the object and the blue shaded areas rep. the back and front. These colors also rep. that they are the same measurements. (e.g the yellow shaded areas are both 5 cm ) this will help you to find the surface area and volume later on. Surface Area:To find the surface area of a rectangular prism if you find the area of each side on the net all you would have to do is add up each side and get the surface area of a rectangular prism.E.G:( 8 + 8 + 12 + 12 +10 + 10= 60 cm (squared) ) Volume:When finding the volume of a rectangular prism all you have to do is : [ Length X Width X Height ]  measurements.E.G: As you can see all of these problems are easy to solve when you ahve a net and the measurements of the object. [...]



Romulo's BOB

2008-04-15T20:19:38.929-05:00

What I've Learned About Rectangular Prisms/CubesWhat a Rectangular Prism IsA rectangular prism is a 3D(Three Dimensional)object that has sides called Height, Length, Width and it looks something like the picture below.A rectangular prism has 6 faces and those faces are called Top, Bottom, Front, Back, Left Side and Right Side. We can see all 6 faces when we make a diagram called the Net. The Net is just a diagram showing what the rectangular prism would look like if you opened it up and flattened it out. The Net on the left shows all 6 faces and which ones they are and the Net on the right shows what each side is(Height,Length,Width). The Net helps you find the surface area of the prism.What a Cube isA cube is basically the same thing as a rectangular prism but the Height, Length and Width are all equal.Just like the rectangular prism the cube also has 6 faces. The nets are also similar but the only difference is the sides in the cube are all equal. The net of the cube also helps you find the surface area.How To Find The Surface Area of a Rectangular Prism/CubeOne way of finding the surface area is to divide them into groups and find their areas separately then add them all together. The groups you divide them into are Front/Back, Top/Bottom and Sides(L Side and R Side) because they are both equal and it makes life easier. There are different formulas for each group.The formula for finding Front/Back isArea=2(Height X Length) or A=2(H X L)The formula for finding Top/Bottom isArea= 2(Width X Length) or A=2 (W X L)The formula for finding Sides isArea= 2(Width X Height) or A=2 (W X H)The 2 is there because after you're done answereing the brackets you multiply what you got in the brackets by 2.After you find those you add them all up to get the surface area.The other way to find surface area is to add all the sides up, but that way takes too long.How To Find The Volume of a Rectangular Prism/CubeTo find the volume you can use the formula Length X Width X Height. The formula says it all so i don't think I need to explain it.The other formula is Base X Height. The Base is usually either the Top or Bottom. This formula is also simple so I won't explain it.Solving The Surface Area and the Volume of a Rectangular Prism/Cube[...]



Davids BOB

2008-04-15T02:05:57.495-05:00

What I have learned/know about rectangular prisms. Rectangular prisms are 3 dimensional shapes, and in class we've learned how to find certain things about the rectangular prism. First of all, theres something called the Net, which is just like what the prism would look like if you made it flat.The next thing would be the measurements of the prism, if you look at the net, you can use that to figure out what the length, width, and height of the prism is. You could switch those numbers around though, because any side of the prism could be the bottom or the base because if you were going to cut it it would be the same on each side. So for our prism lets say we have a length of 8cm, width of 5cm, and a hieght of 2cm.We can use those measurements now to figure out the surface area of the prism, so how many square cm are in that net. Its kind of broken up into pieces, but the face of the prism thats on the opposite side will always be the same if we're dealing with rectangles and...stuff. First we would want to figure out how large the top, bottom, left side, right side, front and back are. Height x Length is how you would get the front or the back, you would have to multiply your answer by 2 to get the area of both the front and the back. Height x Width is how you get the right/left sides, also multiple by 2 to get the area of both sides. Length x Width, this is how you would find the area for the top or bottom, again, multiply by 2 to get the area for both, if it was a square then all of the sides would be the same so if you found one out you know the rest. When we've figured out the are of each face on the rectangular prism, we need to add them up to get the surface area of the whole prism. We could add each little thing up, or we can do something like this, 2(hxl)+ 2(hxw)+ 2(lxw)=Surface AreaSo with our rectangle, the surface area would be something like this:2cm x 8cm = 16cm x2 = 32cm squared 2cm x 5cm = 10cm x2 = 20cm squared8cm x 5cm = 40cm x2 = 80cm squared32cm2 +20cm2 +80cm2= 132cm2Thats only one way of doing this, and its pretty simple too because we found the area for all the sides before we added them up.We also learned how to find the volume!There are two ways we could figure out the volume, one was multiply all of the measurments of a rectangular prism. By that I mean Length x Width x Height, not the cm squared but how many cm it was on the side of the rectangular prism. If the prism had a 8cm length, 5cm width, and a 2cm height, then we could do 8cm x 5cm x 2cm = 80cm cubed (we use a little 3 to represent cubed and we use it to know we're talking about something in 3 dimensions). You could do the same thing with a cube except you would have different numbers for the length, width, and height. Another thing we could do is Base x Height, your base is usualy the width x length. This solution is a little different though, you can represent it in a different way. But you would find out what the base is first, so usuing the cube again, it would have a base of 40cm squared, multiplying that by the height (2cm) would get us our volume of 80cm cubed. It would look something like this if you wanted to draw it out.[...]



Chantel's bob

2008-04-14T22:07:15.100-05:00

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How to find the area of a rectangular prism.

1st: find the area of the top and the area of the bottom. LxW.
2nd: find the area of the front and back. HxL=
3rd: find the area of the left side and right side. HxW=

Ex. if H=11
L=5
W=2

F&&B;; 11x5+11x5= 110cm2
LS&&RS;; 11x2+11x2= 44 cm2
T&&B;; 5x2+5x2=20cm2

Then add the answers together.
100cm2+ 44cm2 + 20cm2
= 174cm2

Find the volume of the rectangular prism:

for this you just go length x width x height

Ex.
H= 5cm
L= 3cm
W= 2cm

5 x 3 x 2= 30cm2


That's all
``CHANNY




Megan's bob

2008-04-14T22:31:23.905-05:00

We learned how to find the surface area of a rectangular prism and this is how:First you need to make a net which is a rectangle that is flatten out where you'd be able to see all of the sides, like this.The colours represents which are the same which is found across from each other. (Eg. Red is the same as the Red across from it.)Now measure each side to find how many centimetres that part has. You can just measure one part of each colour since they're all the same. Measure for Height, Length and Width. Once you get the measurements, multiply by 2 to represent the second part of that colour. (Since their are 2 colours that are the same for the same parts.)Next add everything together to get the surface area!Volume of Rectangular PrismFinding the volume is really not such a big deal! Actually, all you have to do is take the measurements of the Length, Width, and Height and multiply them together! Easy right?Same goes for when you're trying to solve a cube!Make a net like you did on the rectangular prism! Finding the surface area of a cube is really easy!! A piece of cake and I'll show you how!A cube has all of the sides equal which means you just have to measure one side and that measurement goes for the Length, Width, and even Height! VOLUME!Same goes for volume! It's just like how we did with the rectangular prism.Hope you guys find this understandable! (especially the colour thingy part! XP) ~megan[...]



Derrick's Bob

2008-04-14T22:27:56.159-05:00

to find the surface area you will need: Area of top and bottom : 2(L x W)Area of front and back : 2(H x L)Area of both sides : 2(H x W)Surface Area = 2(L x W) + 2(H x L) + 2(H x W)A net will help you find theheight, length, and width of thePrism easily.example of how it should look: to find the volume of this cube you will have to follow this simple step:L x W x H - 5cm² x 5cm² x 5cm²= 125cm² = volume of the cubeAnother step you can try is base times height: ( 25cm² ) x 5cm² = 125cm²[...]



vina's bob

2008-04-14T21:37:19.301-05:00

Vina's bob



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Surface Area:

To find the surface area of a cube or a rectangular prism you need to add all squares together.



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Volume:
To find the volume of a cube or a rectangular prism you need to multiply the length x with x height.



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Jordan's BOB

2008-04-14T20:33:33.359-05:00

(image) (image) First you take your rectangular prism and flatten it so you can see all the sides. This is called a net:(image)
Now take the measurements for the height, width and length or each part of the net (top & bottom, left/right side, front & back) and find the area of each. Since the top-bottom, sides and front-back are the same, you only need to measure one part (top, left side and front) then multiply what you get by 2 to represent the bottom, right side and back.

Then you add everything together. There's your surface area. It should look something like this: (image) (image) To find the volume of a rectangular prism, all you need to do is take the length, width and height measurements then multiply them together. Here's an example: (image) Well... I'm done.



Robby's BOB

2008-04-14T21:17:05.845-05:00

For the past 2 weeks, we learned how to find surface area's and volumes of 3-dimensional (3D) objects like rectangular prisms and cubes. Here is how to find the Surface area and Volume of a Rectangular Prism:Surface Area of a Rectangular PrismThis is a Rectangular Prism. You can see the length, width, and height from any angle, meaning it is a meaning it is a 3D object.Surface area is "how much wrapping you need to cover the whole object". So, if you were to cover it, you much wrapping would you need in a unit of measurement (not squared).Our new Rectangular Prism has some measurements attached to it, so we can solve the surface area and Volume.So:Length = 6 cmWidth = 10 cmHeight = 6 cmThere is 1 formula for finding surface area:-It is(Area of L side + Area of R Side) +(Area of Top) + Area of Bottom) +(Area of Front + Area of Back)One important thing must be done to simplify finding the surface area. You must turn the rectangular prism into its 'Net' form, which is as follows:Now do the equation (Since L side and R side, and Top and bottom, and Front and back have the same area, simply x2 to use less space.:Surface Area=(Area of L side x 2) +(Area of Top x 2) +(Area of Front x 2)=(60cm² x 2) + (36cm² x 2)+ (60cm² x 2)=(120cm²) + (72cm²) + (120cm²)=312cm² is the Surface AreaNow Volume is pretty easy, there are 2 different ways on finding it. One is : Length x Width x Heightthe other one is Area of Base x HeightI'll do both to prove they both work:The measurements are:L = 6 cmW = 10 cmH = 6 cmThe Formula:= Length x Width x Height= 6cm x 10 cm x 6 cm= 60 cm x 6= 360 cm³ (note, the answer is CUBED or the power of 3 (³) because you are multiplying 3 dimensions together: length, width, and height)The Second Formula is Area of Base x Height:Area of Base = L x W or L x H or W x HArea of Base = L x W (for now)Area of Base = 6cm x 10cmArea of Base = 60cm²Height = 6cm60cm² x 6 = 360 cm³See, the answer is 360cm³ for both, meaning they both work.The Length x Width x Height one is easier, in my opinion, because it takes less work to do.And that's how you find the volume and surface area of a Rectangular Prism.[...]