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Please solve for r in the equation for surface area of a cylinder.

A = 2*π*r^2  + 2*π*r*h

 Sep 16, 2020
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Solve for r:
A = 2 π h r + 2 π r^2

A = 2 h π r + 2 π r^2 is equivalent to 2 h π r + 2 π r^2 = A:
2 π h r + 2 π r^2 = A

Divide both sides by 2 π:
r^2 + h r = A/(2 π)

Add h^2/4 to both sides:
r^2 + h r + h^2/4 = h^2/4 + A/(2 π)

Write the left hand side as a square:
(r + h/2)^2 = h^2/4 + A/(2 π)

Take the square root of both sides:
r + h/2 = sqrt(h^2/4 + A/(2 π)) or r + h/2 = -sqrt(h^2/4 + A/(2 π))

Subtract h/2 from both sides:
r = sqrt((h^2)/4 + A/(2 π)) - h/2 or r + h/2 = -sqrt(h^2/4 + A/(2 π))

Subtract h/2 from both sides:

r = sqrt((h^2)/4 + A/(2 π)) - h/2 

 Sep 16, 2020

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