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anonymous

  • one year ago

The volume of a cube is 48 cubic feet. What is the volume of a pyramid that fits exactly inside the cube? Provide an explanation and proof for your answer to receive full credit.

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  1. anonymous
    • one year ago
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    The volume of the cone is 1/3 the volume of the cube. I divide 48 by 3 and i get 16. The volume of a pyramid is 1/3 Bh, where B is the area of the base and h is the height. The volume of a cube is a^3 where a is the side of the cube. If a pyramid fits in a cube with side "a", then the base is a square, with sides a by a, and the height is also a.When you find the volume of this pyramid using the formula, you get: V = 1/3 Bh = 1/3 (a * a) * a = 1/3 a^3, which is 1/3 the volume of the cube which was a^3.

  2. anonymous
    • one year ago
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    @is3535 this is what i got but idk if i right at all im not very good at these questions

  3. anonymous
    • one year ago
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    That's correct

  4. anonymous
    • one year ago
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    @M4thM1nd thank you! can u help me with another

  5. anonymous
    • one year ago
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    Sure!

  6. anonymous
    • one year ago
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    Pyramid A is a square pyramid with a base side length of 18 inches and a height of 9 inches. Pyramid B has a volume of 3136 cubic inches. How many times bigger is the volume of pyramid B than pyramid A? Give your answer as a percent. Provide an explanation and proof for your answer to receive full credit.

  7. anonymous
    • one year ago
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    Ok, we know the equation for the pyramid volume, which is: \[V = \frac{1}{3}A_{base}h\]

  8. anonymous
    • one year ago
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    What is the \(A_{base}\) of pyramid A?

  9. xapproachesinfinity
    • one year ago
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    your answer is good \[V_{pyramid}=\frac{1}{3}a^3=\frac{1}{3}V_{cube}\]

  10. xapproachesinfinity
    • one year ago
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    you reasoning is just perfect :)

  11. anonymous
    • one year ago
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    thank you! @xapproachesinfinity one sec @M4thM1nd im going to try this on my own then ppst what i got is that okay??

  12. anonymous
    • one year ago
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    Okay ^^

  13. anonymous
    • one year ago
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    umm so this is what i got so far I got the volume of Pyramid A: Pyramid A's volume is 972 because V = Base side length^2 x h/3 V = 18^2 x 9/3 = 972.

  14. anonymous
    • one year ago
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    That's right!

  15. anonymous
    • one year ago
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    okay so then do i divide the smaller number by the larger number then multiply that by 100 and round if needed

  16. anonymous
    • one year ago
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    Now, we know the volume of pyramid B, 3136 in^3, what is the percentage difference?

  17. anonymous
    • one year ago
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    then i get 972/3136 = 0.30994898 x 100 = 30.99. So would it be 31% or 30%?

  18. anonymous
    • one year ago
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    that's it xD

  19. anonymous
    • one year ago
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    31%

  20. anonymous
    • one year ago
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    thank you sooo much!!! i have a few more let me finish typing out this questions answer in my quize then ill post another if you can still help me?!?!

  21. anonymous
    • one year ago
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    No problem ^^

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