A cell phone telecommunication tower stands in the shape of a rectangular pyramid. The tower stands 80 m tall and rests on a base that is 15 m by 20 m. What is the volume of the tower?(1 point) Responses 12,000 m3 12,000 m cubed 70 m3 70 m cubed 24,000 m3 24,000 m cubed 8,000 m3

1 answer

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

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

First, we need to calculate the base area of the pyramid. The base is a rectangle, so the area can be found using:

\[ \text{Base Area} = \text{Length} \times \text{Width} = 15 , \text{m} \times 20 , \text{m} = 300 , \text{m}^2 \]

Next, we substitute the base area and height into the volume formula. The height of the pyramid is given as 80 m.

\[ \text{Volume} = \frac{1}{3} \times 300 , \text{m}^2 \times 80 , \text{m} \]

Calculating this gives:

\[ \text{Volume} = \frac{1}{3} \times 300 \times 80 = \frac{1}{3} \times 24000 = 8000 , \text{m}^3 \]

Therefore, the volume of the tower is \(8000 , \text{m}^3\).

The correct answer is 8,000 m cubed.