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 and a square base with side to impress your egyptian subjects, find the volume of the pyramid using integration.

Answer 1

The volume of your pyramid is approximately
`\(7,066,521,666.7 \ \text{cubic units}\)`.

How did we get the value?

Let us use the formula for the volume of a pyramid:

`\[V = (1)/(3)s^2h\]`

Plug in the values:

`\[V = (1)/(3)(2410)^2(3650)\]`

Now, calculate the result:

`\[V = (1)/(3)(5808100)(3650)\]`

`\[V = (1)/(3)(21,199,565,000)\]`

`\[V = 7,066,521,666.666 \ \text{cubic units}\]`

Therefore, the volume of your pyramid is approximately
`\(7,066,521,666.666 \ \text{cubic units}\)`.

Complete question:

You wake up one morning and find yourself wearing a toga and a scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharaoh. You decide to honor yourself with a pyramid of your own design. You decide it should have a height of 3650 and a square base with sides of 2410 to impress your Egyptian subjects. Find the volume of the pyramid.