197k views
2 votes
S=2πrh+2πr²
solve for h

I need the formula for h. please help!

1 Answer

1 vote
The answer: " h =
(S)/(2 \pi r) − r
" .
_________________________________________________
Step-by-step 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 =
(S)/(2 \pi r) − r
.
____________________________________________________
User Bornander
by
6.1k points