Question

Keon was wondering one day what the volume of the Eiffel Tower would be if the sides were solid. The base is a square with sides measuring 125 m long on each side, and the altitude of the square pyramid is 324 m. What would the volume be in cubic meters?

Answer 1

To find the volume of a square pyramid, we can use the formula for the volume of a pyramid:

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

In this case, the base of the pyramid is a square with sides measuring 125 m. First, we calculate the area of the base:

\[
\text{Base Area} = \text{side}^2 = 125 \, \text{m} \times 125 \, \text{m} = 15625 \, \text{m}^2
\]

Next, the height (altitude) of the pyramid is given as 324 m. Now we can plug the values into the volume formula:

\[
V = \frac{1}{3} \times 15625 \, \text{m}^2 \times 324 \, \text{m}
\]

Calculating the product of the base area and height:

\[
15625 \, \text{m}^2 \times 324 \, \text{m} = 5062500 \, \text{m}^3
\]

Now, we can find the volume:

\[
V = \frac{1}{3} \times 5062500 \, \text{m}^3 = 1687500 \, \text{m}^3
\]

Thus, the volume of the Eiffel Tower, assuming it as a solid square pyramid with the given dimensions, is

\[
\boxed{1687500} \, \text{cubic meters}
\]