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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.

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  1. mathstudent55
    • one year ago
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    Do you know how to calculate the volume of a prism?

  2. anonymous
    • one year ago
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    no

  3. mathstudent55
    • one year ago
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    Ok. Here it is: V = LWH The volume is the length multiplied by the width multiplied by the height.

  4. mathstudent55
    • one year ago
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    Here is an example: |dw:1435895710114:dw|

  5. mathstudent55
    • one year ago
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    Now you can find the volumes of the two prisms you are given.

  6. mathstudent55
    • one year ago
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    What is 4 * 5 * 8 = ? What is 10 * 8 * 2 = ?

  7. anonymous
    • one year ago
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    160 and 160

  8. mathstudent55
    • one year ago
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    Correct. That means both of the volumes are the same. That means the answer is not choices A or D.

  9. mathstudent55
    • one year ago
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    Now we need to find the surface areas of both prisms. Do you know how to calculate the surface area of a prism?

  10. anonymous
    • one year ago
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    no

  11. mathstudent55
    • one year ago
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    A prism has 6 sides. We need to find the areas of all six sides and add them all up.

  12. mathstudent55
    • one year ago
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    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.

  13. anonymous
    • one year ago
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    so add all the sides twice

  14. mathstudent55
    • one year ago
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    No. Do only three sides that are different. Add them up and multiply by 2.

  15. anonymous
    • one year ago
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    ok

  16. anonymous
    • one year ago
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    34 and 40

  17. mathstudent55
    • one year ago
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    I'll show you what I mean. |dw:1435896232247:dw|

  18. mathstudent55
    • one year ago
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    The front and back sides are congruent. The area of each one is: 4 cm * 8 cm = 32 cm^2 |dw:1435896290934:dw|

  19. anonymous
    • one year ago
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    could u plz hurry i need to get to bed its 10:02

  20. mathstudent55
    • one year ago
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    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|

  21. mathstudent55
    • one year ago
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    Ok, almost done.

  22. mathstudent55
    • one year ago
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    The top and bottom are congruent. Each has an area of 4 cm * 5 cm = 20 cm^2 |dw:1435896416148:dw|

  23. mathstudent55
    • one year ago
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    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.

  24. mathstudent55
    • one year ago
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    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

  25. anonymous
    • one year ago
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    so its D

  26. mathstudent55
    • one year ago
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    Prism A: 184 cm^2 Prism B: 232 cm^2 Now you can choose between choices B and C.

  27. mathstudent55
    • one year ago
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    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.

  28. anonymous
    • one year ago
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    i mean b

  29. mathstudent55
    • one year ago
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    Great. You got it!

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