Question

1. a regular pyramid has a square base. the perimeter of the base is 48 inches and the height of the pyramid is 15 inches. what is the volume of the pyramid in cubic inches?

Explanation:

Step1: Find side - length of base

Since the base is a square and its perimeter $P = 4s$ (where $s$ is the side - length), and $P = 48$ inches. Then $s=\frac{P}{4}=\frac{48}{4}=12$ inches.

Step2: Calculate base area

The area of a square base $A = s^{2}$. Substituting $s = 12$ inches, we get $A=12^{2}=144$ square inches.

Step3: Calculate volume

The volume formula for a pyramid is $V=\frac{1}{3}Ah$ (where $A$ is the base area and $h$ is the height). Given $A = 144$ square inches and $h = 15$ inches. Then $V=\frac{1}{3}\times144\times15$.
$V = 720$ cubic inches.

Answer:

720 cubic inches