Question

2 a decorative pyramid is placed inside the tank and has a square base of 6 in by 6 in and a height of 9 in. which expression correctly represents the volume of the pyramid, $v=\frac{1}{3}lwh$? ① $\frac{1}{2}(6)(6)(9)$ ② $\frac{1}{3}(6)(9)(9)$ ③ $\frac{1}{2}(6)(9)(9)$ ④ $\frac{1}{2}(6)(6)(9)$

Explanation:

Step1: Identify base and height values

The base of the square - based pyramid has side lengths of 6 inches, so the base area \(B = 6\times6\) (since for a square \(B = s\times s\), where \(s = 6\)), and the height \(h=9\) inches.

Step2: Apply volume formula

The volume formula for a pyramid is \(V=\frac{1}{3}Bh\). Substituting \(B = 6\times6\) and \(h = 9\) into the formula, we get \(V=\frac{1}{3}(6)(6)(9)\).

Answer:

A. \(\frac{1}{3}(6)(6)(9)\)