Question

1. 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. 216 cubic units
c. 432 cubic units
d. 648 cubic units

Explanation:

Step1: Calculate the base area

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

Step2: Use the pyramid volume formula

The volume formula for a pyramid is \(V=\frac{1}{3}A_{base}h\). Here \(A_{base} = 36\) and \(h = 18\). Substitute the values: \(V=\frac{1}{3}\times36\times18\).
First, \(\frac{1}{3}\times36 = 12\). Then \(12\times18=216\).

Answer:

B. 216 cubic units