Question

find the volume of this rectangular pyramid. be sure to include the correct unit in your answer. 9 in 5 in 6 in

Explanation:

Step1: Recall the formula for the volume of a rectangular pyramid.

The volume \( V \) of a rectangular pyramid is given by the formula \( V = \frac{1}{3} \times \text{length} \times \text{width} \times \text{height} \).

Step2: Identify the length, width, and height from the diagram.

From the diagram, the length \( l = 5 \) in, the width \( w = 6 \) in, and the height \( h = 9 \) in.

Step3: Substitute the values into the formula.

Substitute \( l = 5 \), \( w = 6 \), and \( h = 9 \) into the formula:

$$ V = \frac{1}{3} \times 5 \times 6 \times 9 $$

Step4: Perform the calculations.

First, multiply \( 5 \times 6 = 30 \). Then, multiply \( 30 \times 9 = 270 \). Finally, multiply by \( \frac{1}{3} \):

$$ V = \frac{1}{3} \times 270 = 90 $$

Step5: Determine the unit.

The units for length, width, and height are inches, so the unit for volume is cubic inches (\( \text{in}^3 \)).

Answer:

\( 90 \text{ cubic inches} \) or \( 90 \text{ in}^3 \)