Use the formula for the volume of a rectangular pyramid to find the volume of a pyramid-shaped tent whose height is 75 in., width is 111 in., and length is 111 in. when standing.

Responses

308,025 in.3
308,025 in. cubed

33,034.03 in.3
33,034.03 in. cubed

400,000 in.3
400,000 in. cubed

924,075 in.3

1 answer

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:

  1. Calculate the product of the base area and height:

\[ 12,321 , \text{in.}^2 \times 75 , \text{in.} = 924,075 , \text{in.}^3 \]

  1. 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