Question

find the volume of a pyramid with a square base, where the perimeter of the base is 7.3 ft and the height of the pyramid is 6 ft. round your answer to the nearest tenth of a cubic foot.

Explanation:

Step1: Find the side length of the square base

The perimeter of a square is given by \( P = 4s \), where \( s \) is the side length. We know the perimeter \( P = 7.3 \) ft. So, we solve for \( s \):
\( s=\frac{P}{4}=\frac{7.3}{4} = 1.825 \) ft.

Step2: Calculate the area of the square base

The area \( A \) of a square is \( A = s^2 \). Substituting \( s = 1.825 \) ft:
\( A=(1.825)^2= 1.825\times1.825 = 3.330625 \) square feet.

Step3: Use the volume formula for a pyramid

The volume \( V \) of a pyramid is given by \( V=\frac{1}{3}Ah \), where \( A \) is the area of the base and \( h \) is the height. We know \( A = 3.330625 \) sq ft and \( h = 6 \) ft. Substituting these values:
\( V=\frac{1}{3}\times3.330625\times6 \)
First, calculate \( 3.330625\times6 = 19.98375 \)
Then, \( \frac{1}{3}\times19.98375 = 6.66125 \)

Step4: Round to the nearest tenth

Rounding \( 6.66125 \) to the nearest tenth gives \( 6.7 \) (since the hundredth digit is 6, which is greater than or equal to 5, we round up the tenth digit).

Answer:

\( 6.7 \) cubic feet