One of the ancient stone pyramids in Egypt has a square base that measures 146 m on each side. The height is 84 m. What is the volume of the​ pyramid?

Answer 1

To calculate the volume of a pyramid, you can use the following formula:

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

1. Calculate the area of the base: Since the base is square, the area \(A\) can be calculated as: \[ A = \text{side length} \times \text{side length} = 146 , \text{m} \times 146 , \text{m} = 21,316 , \text{m}^2 \]

2. Use the height of the pyramid: The height \(h\) is given as 84 m.

3. Plug these values into the volume formula: \[ V = \frac{1}{3} \times 21,316 , \text{m}^2 \times 84 , \text{m} \]

   Now perform the multiplication: \[ V = \frac{1}{3} \times 1,788,624 , \text{m}^3 \]

4. Finally divide by 3 to find the volume: \[ V = 596,208 , \text{m}^3 \]

So, the volume of the pyramid is \( \boxed{596,208 , \text{m}^3} \).