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Jun 29, 8:51:41 AM

Find the volume of a pyramid with a square base, where the perimeter of the base is
10.7 ft and the height of the pyramid is 9.8 ft. Round your answer to the nearest
tenth of a cubic foot.

User Khriz
by
8.9k points

1 Answer

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9514 1404 393

Answer:

23.4 ft³

Explanation:

In terms of the perimeter of the square base, the volume of a pyramid can be found using the formula ...

V = (1/48)P²h . . . . . where P is the base perimeter and h is the height

V = (1/48)(10.7 ft)²(9.8 ft) ≈ 23.4 ft³

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Additional comment

The relevant formulas usually used are ...

P = 4s . . . . perimeter of a square with side length s

A = s² . . . . area of a square with side length s

V = (1/3)Bh . . . . . volume of a pyramid with base area B and height h

Solving the perimeter equation for s, and using that result in the other formulas, we get ...

s = P/4

B = (P/4)² = P²/16

V = 1/3(P²/16)h = (1/48)P²h . . . . the formula used above

Using this result saves the effort of computing the intermediate values of side length and base area.

User Jammy
by
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