To find the volume of a pyramid, you can use the formula:
\[ V = \frac{1}{3} \times B \times h \]
where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height (altitude) of the pyramid.
In this case, the base of the pyramid is a square with each side measuring 112 feet. Therefore, the area of the base \( B \) is:
\[ B = \text{side} \times \text{side} = 112 , \text{ft} \times 112 , \text{ft} = 12,544 , \text{ft}^2 \]
The altitude \( h \) of the pyramid is 71 feet.
Now, plugging in these values into the volume formula:
\[ V = \frac{1}{3} \times 12,544 , \text{ft}^2 \times 71 , \text{ft} \]
Calculating this:
- First, calculate \( 12,544 , \text{ft}^2 \times 71 , \text{ft} \):
\[ 12,544 \times 71 = 892,624 , \text{ft}^3 \]
- Now, divide this by 3 to get the volume:
\[ V = \frac{892,624}{3} = 297,541.33 , \text{ft}^3 \]
So, the volume of the pyramid at the Louvre Museum is approximately 297,541.33 ft³.
None of the options provided match this value, but the closest one to my calculation is 296,874.67 ft³. If you were asked to choose the response that is most accurate relative to the calculation based on given choices, the answer would be 296,874.67 ft.³.