Question

A cylinder has the same height and radius. The total surface area is 100 pi. Calculate the volume

Answer 1

V=125 pi. I found this by finding the radius then plugging it in for the volume

Answer 2

The formula for Surface Area of a cylinder is 2πrh + 2πr². So solve for the height and radius:

A= 2πrh + 2πr²
because the height is the same as the radius, you can do this:

A=2πr² + 2πr²
combine like terms:

A=4πr²
Plug in your information:

100π = 4πr²
Solve for r:

r= 5

Solve for Volume: (v=πr²h)
Since height is the same as volume, combine like terms:

V=πr³

r³= 125
Plug into the equation:

V=125π