Question

S=2πrh+2πr² solve for h I need the formula for h. please help!

Answer 1

The answer:  "  h  =  $\frac{S}{2 \pi r}$   −   r  " .
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Explanation:
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Given:
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The formula/equation for the "surface area, "S", for a cylinder:
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         S = 2 π r h  +  2 π r²  ; 
 
                           in which:  
                                             S = the surface area ;
                                             r = radius ;
                                             h = height;
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Rearrange the equation; and isolate "h" on ONE side of the equation;
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    So, consider:   
 
              2 π r h  +  2 π r²  ;  
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Factor out a "2 π r " ;
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S = 2 π r * (h + r) ;

Divide each side of the equation by "2 π r " ;
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      S / (2 π r) = [(2 π r) * (h + r)] / [2 π r] ;

to get:  
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      S / (2 π r) = h + r ;

↔  h + r  = S / (2 π r) ;
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          Subtract "r" from EACH side of the equation; to isolate "h" on one side of the equation;  and to rewrite/rearrange the formula in terms of "h" ; 
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               h + r − r = [S / (2 π r)] − r  ;
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to get: 
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                 h  =  $\frac{S}{2 \pi r}$   −   r  .
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