Question

Find the volume of a pyramid with a square base, where the perimeter of the base is 10.1\text{ ft}10.1 ft and the height of the pyramid is 13.4\text{ ft}13.4 ft. Round your answer to the nearest tenth of a cubic foot.

Answer 1

The volume of pyramid is 28.5 cubic feet

Explanation:

Volume of square base pyramid =
`(1)/(3) * \text{Area of base} * Height`

Perimeter of square base =
`4 * Side`

We are given that base of pyramid is 10.1

So,
`4 * Side = 10.1`

`Side = (10.1)/(4)`

Side =2.525 ft

Area of square base =
`Side * Side = 2.525 * 2.525=6.375625 ft^2`

Height of pyramid = 13.4 ft

Volume of square base pyramid =
`(1)/(3) * 6.375625 * 13.4=28.477 ft^3`

Hence The volume of pyramid is 28.5 cubic feet