An illustration shows a rectangular pyramid with length of 7.5 miles, a width of 7 miles, and a perpendicular height of 5 miles. The right and front faces are visible. Edges and faces that are not visible are indicated by dashed lines.

Question

What is the volume of the rectangular pyramid?

(1 point)

Answer 1

To find the volume of a rectangular pyramid, we can use the formula:

\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

1. Calculate the Base Area: The base of the pyramid is a rectangle, and its area is given by the product of its length and width.

   \[ \text{Base Area} = \text{Length} \times \text{Width} = 7.5 , \text{miles} \times 7 , \text{miles} \] \[ \text{Base Area} = 52.5 , \text{square miles} \]

2. Use the Height: The height of the pyramid is given as 5 miles.

3. Calculate the Volume:

   \[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \] \[ \text{Volume} = \frac{1}{3} \times 52.5 , \text{square miles} \times 5 , \text{miles} \] \[ \text{Volume} = \frac{1}{3} \times 262.5 , \text{cubic miles} \] \[ \text{Volume} = 87.5 , \text{cubic miles} \]

Therefore, the volume of the rectangular pyramid is \( \mathbf{87.5 , cubic , miles} \).