SOLUTION: A right circular cylinder has a total surface area of 112(pi). If the height of the cylinder is 10, find the diameter of the base.

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Question 1020868: A right circular cylinder has a total surface area of 112(pi). If the height of the cylinder is 10, find the diameter of the base.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The total surface area, SA, is the sum of the lateral surface area and twice the area of the base, i.e.,
SA = LA + 2B ==> SA = 10(circumference)+ 2B
= 10%2A2%2Api%2Ar%2B+2%2Api%2Ar%5E2+=+20%2Api%2Ar%2B2%2Api%2Ar%5E2
==> 20%2Api%2Ar%2B2%2Api%2Ar%5E2+=+112%2Api
==> r%5E2+%2B+10r+=+56 after making the necessary cancellations,
==> r%5E2+%2B+10r+-+56=0 ==> (r+14)(r-4) = 0
==> r = 4. (r cannot be equal to -14 for obvious reasons.)
==> The diameter of the right circular cylinder is 8.