Question

You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide to honor yourself with a pyramid of your own design. You decide it should have height h = 130 and a square base with side s = 870

To impress your Egyptian subjects, find the volume of the pyramid.

Answer 1

V = 3.28x10⁷

Explanation:

The volume of a pyramid is given by:

`V = (1)/(3)bh`

Where:

b: is the base of the pyramid

h: is the height of the pyramid = 130

The base of the square base of the pyramid is given by:

`b = s^(2)`

Where:

s: is the side of the square base = 870

Thus, the base of the square base of the pyramid is:

`b = s^(2) = (870)^(2) = 7.56 \cdot 10^(5)`

Now, the volume of a pyramid is:

`V = (1)/(3)bh = (1)/(3)(7.56 \cdot 10^(5))*130 = 3.28 \cdot 10^(7)`

Therefore, the volume of the pyramid is 3.28x10⁷.

I hope it helps you!

Answer 2

32799000 cubic units

Explanation:

Height if the Pyramid=130 Units

Side Length of square base=870 Units

Volume of a Pyramid=
`(1)/(3)`* Base Area*Height

Since the base is a square,

Area of a Square of side length s
`=s^2`

Therefore:

Volume
`=(1)/(3)*870^2*130`

=32799000 cubic units

The volume of your pyramid is 32799000 cubic units.