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 formula for the volume \( V \) of a rectangular pyramid is \( V=\frac{1}{3} \times \text{length} \times \text{width} \times \text{height} \). From the diagram, we can identify the length, width, and height. Let's assume the length \( l = 7 \) in, width \( w = 5 \) in, and height \( h = 9 \) in (since the height of the pyramid is given as 9 in, and the base dimensions are 7 in and 5 in).

Step2: Substitute the values into the formula

Substitute \( l = 7 \), \( w = 5 \), and \( h = 9 \) into the formula:

$$ V=\frac{1}{3}\times7\times5\times9 $$

Step3: Simplify the expression

First, multiply \( 7\times5 = 35 \), then \( 35\times9=315 \). Then, \( \frac{1}{3}\times315 = 105 \). The unit for volume is cubic inches (\( \text{in}^3 \)).

Answer:

\( 105 \) cubic inches (or \( 105 \text{ in}^3 \))