SOLUTION: If the surface area of a right circular cylinder is 12pie and the height is 1, what is its radius?

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Question 121083: If the surface area of a right circular cylinder is 12pie and the height is 1, what is its radius?


Answer by solver91311(24713) About Me  (Show Source):
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You don't specify whether you want the lateral surface area or the total surface area:

For the lateral surface area:

A=2%28pi%29rh.

For h+=+1 and A=12%28pi%29, this becomes

2%28pi%29r=12%28pi%29

Divide both sides by 2%28pi%29

r=6

Therefore, if the lateral surface area is 12%28pi%29, then the radius is 6

For the total surface area:

A=2%28pi%29r%5E2%2B2%28pi%29rh, again substituting h+=+1 and A=12%28pi%29, we get:

2%28pi%29r%5E2%2B2%28pi%29r=12%28pi%29

Again, divide by 2%28pi%29

r%5E2%2Br=6

r%5E2%2Br-6=0

Factor

%28r%2B3%29%28r-2%29=0, so r=-3 or r=2.

We can exclude r=-3 because we are looking for a positive number measurement of length.

Therefore if the total surface area is 12%28pi%29, the radius is 2