A three-dimensional illustration of a pyramid.

Question

The pyramid is a light, golden-yellow color, with darker, slightly shaded areas to suggest depth. 

The base of the pyramid is a rectangle, with dimensions labeled as 15 ft and 24 ft.

The apex of the pyramid is connected to the base corners by dashed lines, implying that these unseen edges are part of the structure.

A vertical dashed line extends from the apex to the base, indicating the pyramid's height, which is labeled as 20 feet. what is the volume of the pyramid in cubic feet?

Answer 1

To calculate the volume of a pyramid, you can use the formula:

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

First, we need to determine the base area. The base of the pyramid is a rectangle with dimensions 15 ft and 24 ft.

\[ \text{Base Area} = \text{Length} \times \text{Width} = 15 , \text{ft} \times 24 , \text{ft} = 360 , \text{ft}^2 \]

Now, we can use the height of the pyramid, which is given as 20 ft, to calculate the volume:

\[ \text{Volume} = \frac{1}{3} \times 360 , \text{ft}^2 \times 20 , \text{ft} \]

Calculating it step-by-step:

1. Multiply the base area by the height: \[ 360 , \text{ft}^2 \times 20 , \text{ft} = 7200 , \text{ft}^3 \]

2. Now, divide by 3 to get the volume: \[ \text{Volume} = \frac{7200 , \text{ft}^3}{3} = 2400 , \text{ft}^3 \]

Therefore, the volume of the pyramid is \( \boxed{2400} \) cubic feet.