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)

Question

Responses

8,000 m3
8,000 m cubed

70 m3
70 m cubed

24,000 m3
24,000 m cubed

12,000 m3

Answer 1

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

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

1. Calculate the base area of the rectangular base: The base is 15 m by 20 m, so the area \( A \) is:

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

2. Use the height of the pyramid: The height \( h \) of the pyramid is given as 80 m.

3. Calculate the volume: Substitute the base area and height into the volume formula:

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

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

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

Therefore, the volume of the tower is 8,000 m³.