Volume of Pyramids Quick Check

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Question
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

8,000 m3
8,000 m cubed

24,000 m3

1 answer

The volume \( V \) of a pyramid is calculated using the formula:

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

In this case, the base is a rectangle with dimensions 15 m and 20 m. First, let's calculate the area of the base:

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

The height of the pyramid is given as 80 m. Now we can substitute the values 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.