Quandaries
and Queries 

Who is asking: Parent Level: Middle Question: 

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
and the rectangle has area
Thus
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
which is a linear equation for r. I hope this helps, 

