Use the formula for the volume of a rectangular pyramid to find the volume of a pyramid-shaped tent whose height is 75 in., width is 111 in., and length is 111 in. when standing.(1 point)

Responses

33,034.03 in.3
33,034.03 in. cubed

924,075 in.3
924,075 in. cubed

400,000 in.3
400,000 in. cubed

308,025 in.3

1 answer

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

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

The base area for a rectangular pyramid is calculated as:

\[ \text{Base Area} = \text{Length} \times \text{Width} \]

In this case, the height (h) is 75 in., the width (w) is 111 in., and the length (l) is 111 in.

First, calculate the base area:

\[ \text{Base Area} = 111 \text{ in} \times 111 \text{ in} = 12,321 \text{ in}^2 \]

Next, use the base area and height to find the volume:

\[ V = \frac{1}{3} \times 12,321 \text{ in}^2 \times 75 \text{ in} \]

\[ V = \frac{1}{3} \times 924,075 \text{ in}^3 \]

\[ V = 308,025 \text{ in}^3 \]

Therefore, the volume of the pyramid-shaped tent is 308,025 in³.