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

24,000 m3
24,000 m cubed

12,000 m3
12,000 m cubed

70 m3
70 m cubed

8,000 m3

1 answer

The volume \( V \) of a rectangular pyramid can be calculated using the formula:

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

First, we need to find the area of the base. The base is a rectangle with dimensions 15 m by 20 m. The area \( A \) of the base is:

\[ A = \text{length} \times \text{width} = 15 , \text{m} \times 20 , \text{m} = 300 , \text{m}^2 \]

Now, plug the base area and the height into the volume formula. The height of the pyramid is given as 80 m:

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

Calculating this gives:

\[ V = \frac{1}{3} \times 24000 , \text{m}^3 \]

\[ V = 8000 , \text{m}^3 \]

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