Question 1208904
.
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(highlight(NOT))}}} for the total surface area of a cylinder.


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



<pre>
Your starting formula is 

    T = {{{pi*r*sqrt(r^2 + h^2)}}} + {{{pi*r^2}}}.


Isolate the term with the square root

    T - {{{pi*r^2}}} = {{{pi*r*sqrt(r^2 + h^2)}}}


Divide both sides by {{{pi*r}}}

    {{{(T-pi*r^2)/(pi*r)}}} = {{{sqrt(r^2+h^2)}}}.

    {{{T/(pi*r)-r)}}} = {{{sqrt(r^2+h^2)}}}.


Square both sides

    {{{(T/(pi*r)-r)^2}}} = {{{r^2+h^2}}}.


Express  {{{h^2}}}

    {{{h^2}}} = {{{(T/(pi*r)-r)^2}}} - {{{r^2}}}


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

    h = {{{sqrt((T/(pi*r)-r)^2-r^2)}}}.


It is the desired expression for h.    <U>ANSWER</U>
</pre>

Solved.


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<U>comment from student</U>: A rude mistake? I think you may want to rephrase that comment.



<U>My response</U>: A right reaction from your side would be to say &nbsp;" Deepest &nbsp;THANKS " &nbsp;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, &nbsp;inform your professor or your teacher or your source about this error.



It is the &nbsp;{{{highlight(highlight(ONLY))}}}  &nbsp;{{{highlight(highlight(right))}}}  &nbsp;way to react on my comment &nbsp;{{{highlight(highlight(ADEQUATELY))}}}.