SOLUTION: Find the volume of cylinder of a height 4cm whose total surface area is 484sqcm

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Question 670562: Find the volume of cylinder of a height 4cm whose total surface area is 484sqcm
Found 2 solutions by 44214881, Alan3354:
Answer by 44214881(1) About Me  (Show Source):
You can put this solution on YOUR website!
I'm only in 6th grade. Sorry I really wish I could help you. I need he'll myself

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the volume of cylinder of a height 4cm whose total surface area is 484sqcm
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SA of a cylinder including top and bottom is
SA+=+2%2Api%2Ar%2Ah+%2B+2%2Api%2Ar%5E2
484+=+2%2Api%2Ar%2A4+%2B+2%2Api%2Ar%5E2
484+=+8%2Api%2Ar+%2B+2%2Api%2Ar%5E2
2%2Api%2Ar%5E2+%2B+8pi%2Ar+-+484+=+0
pi%2Ar%5E2+%2B+4pi%2Ar+-+242+=+0
r%5E2+%2B+4r+-+242%2Fpi+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-77.0309924564773+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A1%2A-77.0309924564773=324.123969825909.

Discriminant d=324.123969825909 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+324.123969825909+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+324.123969825909+%29%29%2F2%5C1+=+7.00172163846879
x%5B2%5D+=+%28-%284%29-sqrt%28+324.123969825909+%29%29%2F2%5C1+=+-11.0017216384688

Quadratic expression 1x%5E2%2B4x%2B-77.0309924564773 can be factored:
1x%5E2%2B4x%2B-77.0309924564773+=+%28x-7.00172163846879%29%2A%28x--11.0017216384688%29
Again, the answer is: 7.00172163846879, -11.0017216384688. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-77.0309924564773+%29

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Ignore the -11 solution.
r = 7 (very close to 7)
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Vol+=+pi%2Ar%5E2%2Ah+=+196pi cc
Vol =~ 616 cc