Answer:
[tex]\frac{S.A - 2\pi r^{2} }{2\pi r}[/tex]
Step-by-step explanation:
Formula for the surface area of a cylinder;
Surface area = 2[tex]\pi[/tex]r² + 2[tex]\pi[/tex]rh
Problem:
Make h the subject of the expression;
Solution:
Given expression:
S.A = 2[tex]\pi[/tex]r² + 2[tex]\pi[/tex]rh
Add (- 2[tex]\pi[/tex]r² ) to both sides of the expression:
S.A + ( -2[tex]\pi[/tex]r² ) = ( -2[tex]\pi[/tex]r² ) + 2[tex]\pi[/tex]r² + 2[tex]\pi[/tex]rh
S.A - 2[tex]\pi[/tex]r² = 2 [tex]\pi[/tex]rh
Divide both sides by 2[tex]\pi[/tex]r
[tex]\frac{S.A - 2\pi r^{2} }{2\pi r}[/tex] = [tex]\frac{2\pi rh}{2\pi r}[/tex]
h = [tex]\frac{S.A - 2\pi r^{2} }{2\pi r}[/tex]
