Question

Pyramid A is a right square pyramid with a height of 133m and a square base with a perimeter of 492m. Pyramid B has a square base with a perimeter of 592m and a height of 247m. Which pyramid has the greater volume and by how many times as​ great?

Answer 1

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Answer:

Pyramid B is 2.6888 times the volume of pyramid A

Explanation:

The volume is proportional to the height, and to the square of the linear measure of the base.

Then the ratio of volumes will be ...

B/A = (592²·247)/(492²·133) = 86564608/32194512 ≈ 2.6888

Pyramid B has the greater volume by a factor of about 2.6888.

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Additional comment

The actual volumes in cubic meters will be 1/48 of the numbers we used in the ratio above.

If you recall that the side length is related to the perimeter by ...

P = 4s ⇒ s = P/4

and the volume is ...

V = 1/3s²h

Then you have ...

V = 1/3(P/4)²h = 1/48·P²h . . . . . . P²h is the number we used above