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 (or altitude) of the pyramid.
- Calculate the area of the base (B): Since the base of the pyramid is a square with each side measuring 112 feet, the area \( B \) can be calculated as:
\[ B = \text{side} \times \text{side} = 112 , \text{ft} \times 112 , \text{ft} = 12544 , \text{ft}^2 \]
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Use the altitude (h): The altitude of the pyramid is given as 71 feet.
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Plug the values into the volume formula:
\[ V = \frac{1}{3} \times 12544 , \text{ft}^2 \times 71 , \text{ft} \]
Calculating further:
\[ V = \frac{1}{3} \times 12544 \times 71 \]
First, calculate \( 12544 \times 71 \):
\[ 12544 \times 71 = 891904 \]
Now, divide by 3:
\[ V = \frac{891904}{3} \approx 297301.33 , \text{ft}^3 \]
Thus, the volume of the pyramid at the Louvre Museum is approximately
\[ \boxed{297301.33 , \text{ft}^3} \]