One of the ancient stone pyramids in Egypt has a square base that measures 147 m on each side. The height is 90 m. What is the volume of the​ pyramid?

1 answer

To calculate the volume \( V \) of a pyramid, you can use 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 calculated as:

\[ \text{Base Area} = \text{side}^2 \]

In this case, each side of the square base measures 147 m, so:

\[ \text{Base Area} = 147 , \text{m} \times 147 , \text{m} = 21609 , \text{m}^2 \]

Now, the height of the pyramid is given as 90 m. Thus, we can substitute the base area and height into the volume formula:

\[ V = \frac{1}{3} \times 21609 , \text{m}^2 \times 90 , \text{m} \]

Calculating that gives:

\[ V = \frac{1}{3} \times 1944810 , \text{m}^3 \]

\[ V = 648270 , \text{m}^3 \]

So, the volume of the pyramid is \( 648270 , \text{m}^3 \).