Question

calculate the volume of a square - based pyramid with base sides of 6 units and a height of 18 units.
a. 108 cubic units
b. 648 cubic units
c. 432 cubic units
d. 216 cubic units

Explanation:

Step1: Calculate the base area

The base is a square with side \(s = 6\) units. The area of a square \(A=\ s^{2}\), so \(A = 6^{2}=36\) square units.

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, \(A = 36\) and \(h = 18\). Substitute into the formula: \(V=\frac{1}{3}\times36\times18\).
First, \(\frac{1}{3}\times36 = 12\). Then, \(12\times18=216\).

Answer:

d. 216 cubic units