Question

find the volume of a pyramid with a square base, where the perimeter of the base is 15.2 m and the height of the pyramid is 21.3 m. round your answer to the nearest tenth of a cubic meter.

Explanation:

Step1: Find the side length of the square base

The perimeter of a square is \(P = 4s\), where \(s\) is the side - length. Given \(P=15.2\) m. Then \(s=\frac{P}{4}=\frac{15.2}{4}=3.8\) m.

Step2: Find the area of the square base

The area of a square is \(A = s^{2}\). Substituting \(s = 3.8\) m, we get \(A=(3.8)^{2}=14.44\) \(m^{2}\).

Step3: Use the volume formula for a pyramid

The volume formula for a pyramid is \(V=\frac{1}{3}Ah\), where \(A\) is the base area and \(h\) is the height. Given \(A = 14.44\) \(m^{2}\) and \(h=21.3\) m. Then \(V=\frac{1}{3}\times14.44\times21.3\).
First, calculate \(14.44\times21.3=14.44\times(20 + 1.3)=14.44\times20+14.44\times1.3=288.8+18.772 = 307.572\).
Then \(V=\frac{307.572}{3}=102.524\).

Answer:

\(102.5\) cubic meters