Question

find the volume of this rectangular pyramid. be sure to include the correct unit in your answer. 9 in 7 in 8 in

Explanation:

Step1: Recall the volume formula for a rectangular pyramid

The volume \( V \) of a rectangular pyramid is given by the formula \( V=\frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height of the pyramid. The base of a rectangular pyramid is a rectangle, so the area of the base \( B = l\times w \), where \( l \) is the length and \( w \) is the width of the base.

Step2: Calculate the area of the base

From the diagram, the length \( l = 8\) in and the width \( w = 7\) in. So the area of the base \( B=8\times7 = 56\) square inches.

Step3: Identify the height of the pyramid

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

Step4: Calculate the volume of the pyramid

Substitute \( B = 56\) and \( h = 9\) into the volume formula \( V=\frac{1}{3}Bh \). So \( V=\frac{1}{3}\times56\times9 \). First, calculate \( 56\times9 = 504 \), then \( \frac{1}{3}\times504=168 \).

Answer:

\( 168 \) cubic inches or \( 168\ \text{in}^3 \)