## anonymous one year ago 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.

1. anonymous
2. mathstudent55

Do you know how to calculate the volume of a prism?

3. anonymous

no

4. mathstudent55

Ok. Here it is: V = LWH The volume is the length multiplied by the width multiplied by the height.

5. mathstudent55

Here is an example: |dw:1435895710114:dw|

6. mathstudent55

Now you can find the volumes of the two prisms you are given.

7. mathstudent55

What is 4 * 5 * 8 = ? What is 10 * 8 * 2 = ?

8. anonymous

160 and 160

9. mathstudent55

Correct. That means both of the volumes are the same. That means the answer is not choices A or D.

10. mathstudent55

Now we need to find the surface areas of both prisms. Do you know how to calculate the surface area of a prism?

11. anonymous

no

12. mathstudent55

A prism has 6 sides. We need to find the areas of all six sides and add them all up.

13. 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.

14. anonymous

so add all the sides twice

15. mathstudent55

No. Do only three sides that are different. Add them up and multiply by 2.

16. anonymous

ok

17. anonymous

34 and 40

18. mathstudent55

I'll show you what I mean. |dw:1435896232247:dw|

19. mathstudent55

The front and back sides are congruent. The area of each one is: 4 cm * 8 cm = 32 cm^2 |dw:1435896290934:dw|

20. anonymous

could u plz hurry i need to get to bed its 10:02

21. 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|

22. mathstudent55

Ok, almost done.

23. mathstudent55

The top and bottom are congruent. Each has an area of 4 cm * 5 cm = 20 cm^2 |dw:1435896416148:dw|

24. 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.

25. 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

26. anonymous

so its D

27. mathstudent55

Prism A: 184 cm^2 Prism B: 232 cm^2 Now you can choose between choices B and C.

28. 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.

29. anonymous

i mean b

30. mathstudent55

Great. You got it!