An illustration shows a 3 D pyramid with a rectangular base. The length, width, and height measurements are labeled. The sides on the front that are visible are shown as solid lines and the sides at the back are shown as dashed lines. The base length is labeled 24 feet and the width is labeled 15 feet. The height is shown as a dotted perpendicular line from the top vertex to the base and is labeled 20 feet. The dotted line continues to the base length to make a right angle.

Question

What is the volume of the pyramid in cubic feet?

Answer 1

To calculate the volume of a pyramid, you can use the following 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 with a length of 24 feet and a width of 15 feet. The area \(A\) of the base is given by:

   \[ A = \text{Length} \times \text{Width} = 24 , \text{feet} \times 15 , \text{feet} = 360 , \text{square feet} \]

2. Use the height: The height of the pyramid is given as 20 feet.

3. Substitute the values into the volume formula: Now plug the base area and height into the volume formula:

   \[ \text{Volume} = \frac{1}{3} \times 360 , \text{square feet} \times 20 , \text{feet} \]

   \[ \text{Volume} = \frac{1}{3} \times 7200 , \text{cubic feet} \]

   \[ \text{Volume} = 2400 , \text{cubic feet} \]

Thus, the volume of the pyramid is 2400 cubic feet.