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

Answer:

The height is 0.2003ft

Step-by-step 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

$h = 11.32/56.52$

$h = 0.2003ft$