SOLUTION: calculate a diameter of a solid cylinder which has height of 82cm and total surface area of 2square meter

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Question 996793: calculate a diameter of a solid cylinder which has height of 82cm and total surface area of 2square meter
Answer by Alan3354(69443) About Me  (Show Source):
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calculate a diameter of a solid cylinder which has height of 82cm and total surface area of 2square meter
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Total area = lateral area + 2 ends
= 2pi%2Ar%2Ah+%2B+2pi%2Ar%5E2
2 sq meters = 20000 sq cms
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2pi%2Ar%2Ah+%2B+2pi%2Ar%5E2+=+20000
pi%2Ar%2Ah+%2B+pi%2Ar%5E2+=+10000
82r+%2B+r%5E2+=+10000%2Fpi
r%5E2+%2B+82r+-+10000%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%2B82x%2B-3183.09886183791+=+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=%2882%29%5E2-4%2A1%2A-3183.09886183791=19456.3954473516.

Discriminant d=19456.3954473516 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-82%2B-sqrt%28+19456.3954473516+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2882%29%2Bsqrt%28+19456.3954473516+%29%29%2F2%5C1+=+28.7430918574586
x%5B2%5D+=+%28-%2882%29-sqrt%28+19456.3954473516+%29%29%2F2%5C1+=+-110.743091857459

Quadratic expression 1x%5E2%2B82x%2B-3183.09886183791 can be factored:
1x%5E2%2B82x%2B-3183.09886183791+=+%28x-28.7430918574586%29%2A%28x--110.743091857459%29
Again, the answer is: 28.7430918574586, -110.743091857459. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B82%2Ax%2B-3183.09886183791+%29

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Ignore the negative solution
r = 28.743 cm
d = 57.486 cm