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.(1 point) Responses 33,034.03 in.3 33,034.03 in. cubed 400,000 in.3 400,000 in. cubed 924,075 in.3 924,075 in. cubed 308,025 in.3

1 answer

To find the volume of a rectangular pyramid, you can use the formula:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

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