Question

the formula for the volume, v, of a pyramid is $v=\frac{1}{3}bh$, where b is the area of the base of the pyramid and h is the pyramids height. the base of the pyramid shown has a length of 9 m and a width of 8 m. the height of the pyramid is 12 m. what is the volume of the pyramid? a. $136m^{3}$ b. $256m^{3}$ c. $288m^{3}$ d. $324m^{3}$

Explanation:

Step1: Calculate the area of the base

The base is a rectangle. The area formula for a rectangle is \(B = length\times width\). Given \(length = 9m\) and \(width = 8m\), then \(B=9\times8 = 72m^{2}\).

Step2: Substitute into the volume formula

The volume formula of a pyramid is \(V=\frac{1}{3}Bh\). We know \(B = 72m^{2}\) and \(h = 12m\). Substitute these values into the formula: \(V=\frac{1}{3}\times72\times12\).
First, calculate \(\frac{1}{3}\times72\): \(\frac{1}{3}\times72 = 24\).
Then, calculate \(24\times12\): \(24\times12=288m^{3}\).

Answer:

C. \(288m^{3}\)