anonymous
  • anonymous
Which is true about the volume or surface area of these prisms? A. The volume of A is greater than the volume of B. B. The surface area of B is greater than the surface area of A. C. The surface area of A is greater than the surface area of B. D. The volume of B is greater than the volume of A.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
http://static.k12.com/calms_media/media/395500_396000/395712/2/31a6fdaf83c553b50690ff8bfe66efa86ba322ab/53259_question.jpg
mathstudent55
  • mathstudent55
Do you know how to calculate the volume of a prism?
anonymous
  • anonymous
no

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mathstudent55
  • mathstudent55
Ok. Here it is: V = LWH The volume is the length multiplied by the width multiplied by the height.
mathstudent55
  • mathstudent55
Here is an example: |dw:1435895710114:dw|
mathstudent55
  • mathstudent55
Now you can find the volumes of the two prisms you are given.
mathstudent55
  • mathstudent55
What is 4 * 5 * 8 = ? What is 10 * 8 * 2 = ?
anonymous
  • anonymous
160 and 160
mathstudent55
  • mathstudent55
Correct. That means both of the volumes are the same. That means the answer is not choices A or D.
mathstudent55
  • mathstudent55
Now we need to find the surface areas of both prisms. Do you know how to calculate the surface area of a prism?
anonymous
  • anonymous
no
mathstudent55
  • mathstudent55
A prism has 6 sides. We need to find the areas of all six sides and add them all up.
mathstudent55
  • mathstudent55
There are a few shortcuts we can take. A rectangular prism always has 3 sides congruent to the other three sides. Opposite sides are congruent.
anonymous
  • anonymous
so add all the sides twice
mathstudent55
  • mathstudent55
No. Do only three sides that are different. Add them up and multiply by 2.
anonymous
  • anonymous
ok
anonymous
  • anonymous
34 and 40
mathstudent55
  • mathstudent55
I'll show you what I mean. |dw:1435896232247:dw|
mathstudent55
  • mathstudent55
The front and back sides are congruent. The area of each one is: 4 cm * 8 cm = 32 cm^2 |dw:1435896290934:dw|
anonymous
  • anonymous
could u plz hurry i need to get to bed its 10:02
mathstudent55
  • mathstudent55
The left side and the right side are congruent. Each has an area of: 5 cm * 8 cm = 40 cm^2 |dw:1435896339020:dw| |dw:1435896356529:dw|
mathstudent55
  • mathstudent55
Ok, almost done.
mathstudent55
  • mathstudent55
The top and bottom are congruent. Each has an area of 4 cm * 5 cm = 20 cm^2 |dw:1435896416148:dw|
mathstudent55
  • mathstudent55
Add the 3 faces together and multiply by 2 to get: (32 cm^2 + 40 cm^2 + 20 cm^2 ) * 2 = 92 cm^2 * 2 = 184 cm^2 That is for prism A.
mathstudent55
  • mathstudent55
If you do the same with prism B you get: 2 * ( 10 * 2 + 8 * 2 + 10 * 8) = 2 * (20 + 16 + 80) = 2 * 116 = 232, o3 232 cm^2
anonymous
  • anonymous
so its D
mathstudent55
  • mathstudent55
Prism A: 184 cm^2 Prism B: 232 cm^2 Now you can choose between choices B and C.
mathstudent55
  • mathstudent55
No. D deals with volume. We know the volumes are the same. You need to choose between B and C which deal with surface area.
anonymous
  • anonymous
i mean b
mathstudent55
  • mathstudent55
Great. You got it!

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