QuestionJune 10, 2026

51. Find the volume of a pyramid with a square base, where the perimeter of the base is 15.8 ft and the height of the pyramid is 20.4 ft. Round your answer to the nearest tenth of a cubic foot.

51. Find the volume of a pyramid with a square base, where the perimeter of the base is 15.8 ft and the height of the pyramid is 20.4 ft. Round your answer to the nearest tenth of a cubic foot.
51. Find the volume of a pyramid with a square base,
where the perimeter of the base is 15.8 ft and the height
of the pyramid is 20.4 ft. Round your answer to the
nearest tenth of a cubic foot.

Solution
4.6(124 votes)

Answer

106.1 cubic feet Explanation 1. Determine the side length of the square base Divide the perimeter by 4: s = \frac{15.8}{4} = 3.95 ft. 2. Calculate the area of the base Use the area formula for a square: A = s^2 = 3.95^2 = 15.6025 sq ft. 3. Calculate the volume of the pyramid Apply the volume formula V = \frac{1}{3}Bh, where B is the base area and h is the height: V = \frac{1}{3} \times 15.6025 \times 20.4 = 106.097 cubic ft. 4. Round to the nearest tenth Rounding 106.097 to the nearest tenth gives 106.1.

Explanation

1. Determine the side length of the square base<br />Divide the perimeter by 4: $s = \frac{15.8}{4} = 3.95$ ft.<br /><br />2. Calculate the area of the base<br />Use the area formula for a square: $A = s^2 = 3.95^2 = 15.6025$ sq ft.<br /><br />3. Calculate the volume of the pyramid<br />Apply the volume formula $V = \frac{1}{3}Bh$, where $B$ is the base area and $h$ is the height:<br />$V = \frac{1}{3} \times 15.6025 \times 20.4 = 106.097$ cubic ft.<br /><br />4. Round to the nearest tenth<br />Rounding $106.097$ to the nearest tenth gives $106.1$.
Click to rate:

Similar Questions