The formula A=2*pi*r^2+2*pi*r*h, is the formula for the surface area of a cylinder. An article on math.com goes into more detail of how this formula works.

The u.r.l. is, http://www.math.com/tables/geometry/surfareas.htm .

To solve for r, first rearrange as 2*pi*r^2+2*pi*r*h=A. Divide by 2pi giving

r^2+r*h=A/2pi. Since a^2+2ab+b^2 = (a+b)^2 to complete the square in r^2+r*h, we add (h/2)^2 to both sides, r^2+r*h+h^2/4=A/(2pi)+h^2/4.

Next we factor the left side as (r+h/2)^2 combine the fractions on the right, 2*A+pi*h^2/4*pi

and squaring both sides gives us, r = sqrt(2*A+pi*h^2/4*pi)-h/2. Comments and or corrections are welcomed.

The u.r.l. is, http://www.math.com/tables/geometry/surfareas.htm .

To solve for r, first rearrange as 2*pi*r^2+2*pi*r*h=A. Divide by 2pi giving

r^2+r*h=A/2pi. Since a^2+2ab+b^2 = (a+b)^2 to complete the square in r^2+r*h, we add (h/2)^2 to both sides, r^2+r*h+h^2/4=A/(2pi)+h^2/4.

Next we factor the left side as (r+h/2)^2 combine the fractions on the right, 2*A+pi*h^2/4*pi

and squaring both sides gives us, r = sqrt(2*A+pi*h^2/4*pi)-h/2. Comments and or corrections are welcomed.

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