SOLUTION: Let T = total surface area of a cylinder. Solve T = pi•r•sqrt{r^2 + h^2} + pi•r^2 for h.

Algebra ->  Surface-area -> SOLUTION: Let T = total surface area of a cylinder. Solve T = pi•r•sqrt{r^2 + h^2} + pi•r^2 for h.       Log On


   

Question 1208904: Let T = total surface area of a cylinder.

Solve T = pi•r•sqrt{r^2 + h^2} + pi•r^2 for h.


Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
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 highlight%28highlight%28NOT%29%29 for the total surface area of a cylinder.

        This formula is for the total surface area of a cone. 


Your starting formula is 

    T = pi%2Ar%2Asqrt%28r%5E2+%2B+h%5E2%29 + pi%2Ar%5E2.


Isolate the term with the square root

    T - pi%2Ar%5E2 = pi%2Ar%2Asqrt%28r%5E2+%2B+h%5E2%29


Divide both sides by pi%2Ar

    %28T-pi%2Ar%5E2%29%2F%28pi%2Ar%29 = sqrt%28r%5E2%2Bh%5E2%29.

    T%2F%28pi%2Ar%29-r%29 = sqrt%28r%5E2%2Bh%5E2%29.


Square both sides

    %28T%2F%28pi%2Ar%29-r%29%5E2 = r%5E2%2Bh%5E2.


Express  h%5E2

    h%5E2 = %28T%2F%28pi%2Ar%29-r%29%5E2 - r%5E2


Take the square root of both sides and use its positive value

    h = sqrt%28%28T%2F%28pi%2Ar%29-r%29%5E2-r%5E2%29.


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  highlight%28highlight%28ONLY%29%29  highlight%28highlight%28right%29%29  way to react on my comment  highlight%28highlight%28ADEQUATELY%29%29.