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 of the pyramid can be calculated using the formula:
\[ \text{base area} = \text{length} \times \text{width} \]
In this case, the dimensions of the pyramid-shaped tent are:
- Height (h) = 75 in.
- Width (w) = 111 in.
- Length (l) = 111 in.
First, 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:
\[ V = \frac{1}{3} \times 12,321 , \text{in.}^2 \times 75 , \text{in.} \]
Now calculate 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 (also written as 308,025 in. cubed).