Volume of Pyramids Practice

Question

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Question
Leon 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?(1 point)

Answer 1

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.

1. Calculate the area of the base (B): Since the base is a square with each side measuring 125 m:

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

2. Take the height (h) of the pyramid: The altitude \( h \) is given as 324 m.

3. Now apply the formula:

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

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

   \[ V = 1687500 , \text{m}^3 \]

Thus, the volume of the Eiffel Tower, if it were a solid square pyramid, would be 1,687,500 cubic meters.