To find the volume of a rectangular pyramid, you can use the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
For a rectangular base, the area of the base can be calculated as:
\[ \text{Base Area} = \text{Length} \times \text{Width} \]
In this case:
- Height (h) = 75 inches
- Length (l) = 111 inches
- Width (w) = 111 inches
First, we calculate the base area:
\[ \text{Base Area} = 111 , \text{in.} \times 111 , \text{in.} = 12,321 , \text{in.}^2 \]
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:
\[ V = \frac{1}{3} \times 12,321 \times 75 = \frac{924,075}{3} = 308,025 , \text{in.}^3 \]
Thus, the volume of the pyramid-shaped tent is 308,025 in³.
So the answer is:
308,025 in.³