The " h =
− 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 =
− r .
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