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

924,075 in.3
924,075 in. cubed

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

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

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

1 answer

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)