To find the volume of a rectangular pyramid, you can use the formula:
\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
For a rectangular pyramid, the base area is given by:
\[ \text{Base Area} = \text{Length} \times \text{Width} \]
Given the dimensions of the pyramid-shaped tent:
- Height = 75 in.
- Width = 111 in.
- Length = 111 in.
First, calculate the base area:
\[ \text{Base Area} = 111 , \text{in.} \times 111 , \text{in.} \] \[ \text{Base Area} = 12,321 , \text{in.}^2 \]
Now, substitute the base area and height into the volume formula:
\[ \text{Volume} = \frac{1}{3} \times 12,321 , \text{in.}^2 \times 75 , \text{in.} \] \[ \text{Volume} = \frac{1}{3} \times 924,075 , \text{in.}^3 \] \[ \text{Volume} = 308,025 , \text{in.}^3 \]
Thus, the volume of the pyramid-shaped tent is 308,025 in.³.
The correct answer is 308,025 in.³.