The answer: " h = [tex] \frac{S}{2 \pi r} [/tex] − r " .
_________________________________________________
Explanation:
_________________________________________________
Given:
_________________________________________________
The formula/equation for the "surface area, "S", for a cylinder:
_________________________________________________
S = 2 π r h + 2 π r² ;
in which:
S = the surface area ;
r = radius ;
h = height;
_____________________________________________
Rearrange the equation; and isolate "h" on ONE side of the equation;
__________________________________________________
So, consider:
2 π r h + 2 π r² ;
__________________________________________________
Factor out a "2 π r " ;
__________________________________________________
S = 2 π r * (h + r) ;
Divide each side of the equation by "2 π r " ;
__________________________________________________
S / (2 π r) = [(2 π r) * (h + r)] / [2 π r] ;
to get:
__________________________________________________
S / (2 π r) = h + r ;
↔ h + r = S / (2 π r) ;
__________________________________________________
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" ;
____________________________________________________
h + r − r = [S / (2 π r)] − r ;
____________________________________________________
to get:
____________________________________________________
h = [tex] \frac{S}{2 \pi r} [/tex] − r .
____________________________________________________
