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Let T = total surface area of a cylinder.
Solve T = pi*r*sqrt{r^2 + h^2} + pi*r^2 for h.
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Your post has a rude mistake: this formula is for the total surface area of a cylinder.
This formula is for the total surface area of a cone.
Your starting formula is
T = + .
Isolate the term with the square root
T - =
Divide both sides by
= .
= .
Square both sides
= .
Express
= -
Take the square root of both sides and use its positive value
h = .
It is the desired expression for h. ANSWER
Solved.
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comment from student: A rude mistake? I think you may want to rephrase that comment.
My response: A right reaction from your side would be to say " Deepest THANKS " to me for pointing your error,
and to take all necessary measures to fix your error immediately,
in order for do not spread wrong info in the Internet.
Also, inform your professor or your teacher or your source about this error.
It is the way to react on my comment .