Question

a square prism has a base side length of 8 centimeters and a height of 15 centimeters. what is the volume of a square pyramid with the same base area and height as the prism? use the keypad to type your answer in the box provided. the volume of the pyramid is \boxed{} cubic centimeters.

Explanation:

Step1: Calculate the base area of the square prism (and thus the square pyramid)

The base of the square prism (and pyramid) is a square. The area formula for a square is \(A = s^2\), where \(s\) is the side - length. Given \(s = 8\) cm, then \(A=s^{2}=8^{2}=64\) \(cm^{2}\).

Step2: Recall the volume formula for a square pyramid

The volume formula for a pyramid is \(V=\frac{1}{3}Ah\), where \(A\) is the base area and \(h\) is the height. We know \(A = 64\) \(cm^{2}\) and \(h = 15\) cm.
Substitute the values into the formula: \(V=\frac{1}{3}\times64\times15\).
First, calculate \(64\times15 = 960\). Then, \(V=\frac{960}{3}\).

Step3: Simplify the expression

\(V = 320\) \(cm^{3}\).

Answer:

\(320\)