Question

A reservoir in the shape of a right cylinder has a height of 84 ft am

Answer 1

Question:

A reservoir in the shape of a right circular cylinder has a height of 84ft. If it to contain 79,200 L of water, find its radius.

Answer:

`r = 3.26ft`

Explanation:

Given

`Volume = 79200L` ---- V

`Height = 84ft` --- h

Required

Determine the radius

`Volume = 79200L`

Convert volume to
`ft^3`

`Volume = 79200 * 0.0353147ft^3`

`Volume = 2796.9216ft^3`

The volume (V) of a cylinder is:

`V = \pi r^2 h`

Substitute values for volume and height

`2796.9216 = \pi * r^2 * 84`

Divide both sides by 84

`33.2966857143 = \pi * r^2`

Take
`\pi` as 3.14

`33.2966857143 = 3.14 * r^2`

Divide both sides by 3.14

`10.604 = r^2`

`r^2 = 10.604`

Take the square root of both sides

`r = \sqrt{10.604`

`r = 3.26ft`

Hence, the radius is 3.26 ft