Question

Use the volume formula to determine the volume of the pyramid at the Louvre Museum if it has a base that is
112 feet long on each side and has an altitude of 71 feet.(1 point)

Answer 1

The volume \( V \) of a pyramid can be calculated using the formula:

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

For a pyramid with a square base, the area of the base can be found by squaring the length of one side. Since the base is 112 feet on each side, the area of the base \( A \) is:

\[
A = \text{side}^2 = 112^2 = 12,544 \text{ square feet}
\]

Now, using the height (or altitude) of the pyramid, which is 71 feet, we can substitute the values into the volume formula:

\[
V = \frac{1}{3} \times 12,544 \times 71
\]

Calculating this gives:

\[
V = \frac{1}{3} \times 12,544 \times 71 = \frac{1}{3} \times 891,584
\]

\[
V = 297,194.67 \text{ cubic feet}
\]

Thus, the volume of the pyramid at the Louvre Museum is approximately **297,194.67 cubic feet**.