Question

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

308,025 in.3
308,025 in. cubed

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

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

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

Answer 1

The formula for the volume \( V \) of a rectangular pyramid is given by:

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

Where the Base Area is calculated as:

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

Given:
- Height \( h = 75 \) in.
- Width \( w = 111 \) in.
- Length \( l = 111 \) in.

First, calculate the base area:

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

Now, substitute the base area and height into the volume formula:

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

Calculating the volume:

\[
V = \frac{1}{3} \times 12,321 \times 75 = \frac{924,075}{3} = 308,025 \, \text{in.}^3
\]

Therefore, the volume of the pyramid-shaped tent is:

**308,025 in.³** or **308,025 in. cubed**.