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Volume of Pyramids Quick Check
3 of 53 of 5 Items

Question
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

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

33,034.03 in.3
33,034.03 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:

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

For a rectangular pyramid, the base area is given by:

\[ \text{Base Area} = \text{Length} \times \text{Width} \]

Given the dimensions of the pyramid-shaped tent:

  • Height = 75 in.
  • Width = 111 in.
  • Length = 111 in.

First, calculate the base area:

\[ \text{Base Area} = 111 , \text{in.} \times 111 , \text{in.} \] \[ \text{Base Area} = 12,321 , \text{in.}^2 \]

Now, substitute the base area and height into the volume formula:

\[ \text{Volume} = \frac{1}{3} \times 12,321 , \text{in.}^2 \times 75 , \text{in.} \] \[ \text{Volume} = \frac{1}{3} \times 924,075 , \text{in.}^3 \] \[ \text{Volume} = 308,025 , \text{in.}^3 \]

Thus, the volume of the pyramid-shaped tent is 308,025 in.³.

The correct answer is 308,025 in.³.