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Pyramid A is a square pyramid with a base side length of 12 inches and a height of 8 inches. Pyramid B has a volume of 3,456 cubic inches. How many times bigger is the volume of pyramid B than pyramid A? Give your answer as a percentage. Provide an explanation and proof for your answer to receive full credit.



Answer :

sqdancefan

Answer:

  900% times as big

Step-by-step explanation:

You want the ratio of the volume of Pyramid B, which is 3456 in³, to that of Pyramid A, which is 12 in square and 8 in high, expressed as a percentage.

Pyramid A

The volume of Pyramid A is found by ...

  [tex]V=\dfrac{1}{3}s^2h\\\\\\V=\dfrac{1}{3}(12\text{ in}^2)(\text{$8$ in})=384\text{ in}^3[/tex]

Bigger

The volume of Pyramid B is larger by a factor of ...

  [tex]\dfrac{\text{Volume B}}{\text{Volume A}}=\dfrac{3456\text{ in}^3}{384\text{ in}^3}=9=9\times100\%=\boxed{900\%}[/tex]

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