Question

The surface area of a cylinder is 520 ft.² The area of one of the bases is 254.34 ft.² find the height of the cylinder

Answer 1

The height is 0.2003ft

Explanation:

Given

`Surface\ Area = 520`

`Base\ Area = 254.34`

Required

The height of the cylinder

The base area of the cylinder is:

`Base\ Area = \pi r^2`

This gives

`254.34 = 3.14 * r^2`

Divide by 3.14

`81 = r^2`

Take square root of both sides

`r = \sqrt{81`

`r = 9`

The surface area of a cylinder is:

`Surface\ Area = 2\pi rh + 2\pi r^2`

This gives

`520 = 2*3.14* 9h + 2*3.14* 9^2`

`520 = 56.52h + 508.68`

Collect like terms

`56.52h = 520 -508.68`

`56.52h = 11.32`

Solve for h

`h = 11.32/56.52`

`h = 0.2003ft`