To find the volume of a rectangular pyramid, you can use the formula:
\[ V = \frac{1}{3} \cdot \text{Base Area} \cdot \text{Height} \]
For a rectangular base, the base area can be calculated as:
\[ \text{Base Area} = \text{Length} \cdot \text{Width} \]
In this case, the dimensions of the pyramid-shaped tent are:
- Height (h) = 75 in.
- Width (w) = 111 in.
- Length (l) = 111 in.
Now, let's calculate the base area:
\[ \text{Base Area} = 111 , \text{in} \cdot 111 , \text{in} = 12,321 , \text{in}^2 \]
Next, we can use this base area to find the volume:
\[ V = \frac{1}{3} \cdot 12,321 , \text{in}^2 \cdot 75 , \text{in} \]
Now, we multiply the base area by the height:
\[ 12,321 , \text{in}^2 \cdot 75 , \text{in} = 924,075 , \text{in}^3 \]
Now, divide by 3:
\[ V = \frac{1}{3} \cdot 924,075 , \text{in}^3 = 308,025 , \text{in}^3 \]
So, the volume of the pyramid-shaped tent is:
\[ \text{308,025 in.}^3 \]
Thus, the correct response is:
308,025 in.3 (or 308,025 in. cubed)