Question

A cylinder has a surface area of 5652 square millimeters. If the diameter of the cylinder is 30 millimeters, what is the height? Please show work

Answer 1

45 m

Explanation:

Answer 2

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(radius is half the diameter, 30/2 = 15):


`\sf 5652\approx 2(3.14)(15)h+2(3.14)(15)^2`

Simplify:


`\sf 5652\approx 94.2h+1413`

Subtract 1413 to both sides:


`\sf 4239\approx 94.2h`

Divide 94.2 to both sides:


`\boxed{\sf h\approx 45~mm}`

So the height is approximately 45 millimeters.