Question

Find the height of a cylinder if the surface area is 402 square centimeters and the radius is 4 centimeters. Round to the nearest tenth. Please show work

Answer 1

The formula for the surface area of a cylinder is:


`\sf A=2\pi rh+2\pi r^2`

Plug in what we know, use 3.14 to approximate for pi:


`\sf 402\approx 2(3.14)(4)h+2(3.14)(4)^2`

Simplify:


`\sf 402\approx 25.12h+100.48`

Subtract 100.48 to both sides:


`\sf 301.52\approx 25.12h`

Divide 25.12 to both sides:


`\sf h\approx\boxed{\sf 12.0~cm}`

So the height is approximately 12 centimeters.