Hi Kathryn,

Think about the reverse. If you had all the information you needed, how would you find the surface area of a cylinder. I am going to do this assuming that the surface area of the cylinder includes the ends. If the surface area doesn't include the ends it is earier.

I think of a cylinder as a soup can. Use your can opener and cut off the ends and then cut vertically up the cylindrical piece that remains and roll it out flat. I have labeled the radius of the cylinder and its height.

This gives you three pieces, two circular disks and a rectangle.

The disks each have area

pi r²

and the rectangle has area

2 pi r h

Thus

surface area = 2 pi r² + 2 pi r h

If you know the surface area and the height of the cylinder substitute these values and you have a quadratic equation for r.

If your value for the surface area does not include the ends then you have

surface area = 2 pi r h

which is a linear equation for r.

I hope this helps,
Penny

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