Question

find the volume of this rectangular pyramid. be sure to include the correct unit in your answer.

Explanation:

Step1: Recall the volume formula for a rectangular pyramid

The volume \( V \) of a rectangular pyramid is given by \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height of the pyramid.

Step2: Calculate the area of the base

The base of the rectangular pyramid is a rectangle with length \( l = 6\) in and width \( w = 4\) in. The area of a rectangle is \( B=l\times w \), so \( B = 6\times4=24\) \( \text{in}^2 \).

Step3: Identify the height of the pyramid

The height \( h \) of the pyramid is given as \( 9 \) in.

Step4: Substitute the values into the volume formula

Substitute \( B = 24\) \( \text{in}^2 \) and \( h = 9\) in into the formula \( V=\frac{1}{3}Bh \). So \( V=\frac{1}{3}\times24\times9 \).

First, calculate \( \frac{1}{3}\times24 = 8 \), then \( 8\times9=72 \).

Answer:

\( 72 \) cubic inches (or \( 72\ \text{in}^3 \))