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 can be calculated using the length and width. In this case, the base area (A) of the pyramid-shaped tent is calculated as follows:
\[ A = \text{Length} \times \text{Width} = 111 , \text{in.} \times 111 , \text{in.} = 12,321 , \text{in.}^2 \]
Now, we will plug the base area and the height into the formula for the volume:
\[ V = \frac{1}{3} \times 12,321 , \text{in.}^2 \times 75 , \text{in.} \]
Calculating this step by step:
- Calculate the product of the base area and height:
\[ 12,321 , \text{in.}^2 \times 75 , \text{in.} = 924,075 , \text{in.}^3 \]
- Now apply the \(\frac{1}{3}\):
\[ V = \frac{1}{3} \times 924,075 , \text{in.}^3 = 308,025 , \text{in.}^3 \]
Thus, the volume of the pyramid-shaped tent is 308,025 in³.
So, the correct response is:
308,025 in.³ 308,025 in. cubed