Question

a right square pyramid has a base with side lengths of 3 centimeters. the height of the pyramid is 7 centimeters. what is the volume, in cubic centimeters, of this pyramid?
a 7
b 14
c 21
d 63

Explanation:

Step1: Calculate the base area

The base is a square with side length \(a = 3\) cm. The area of a square \(A=a^{2}\), so \(A = 3^{2}=9\) \(cm^{2}\).

Step2: Use the pyramid volume formula

The volume formula for a pyramid is \(V=\frac{1}{3}Ah\), where \(A\) is the base area and \(h\) is the height. Here \(A = 9\) \(cm^{2}\) and \(h = 7\) cm. Then \(V=\frac{1}{3}\times9\times7\).
First, \(\frac{1}{3}\times9 = 3\), then \(3\times7=21\) \(cm^{3}\).

Answer:

C. 21