Question

Solve the formula for the indicated variableArea of a cylinder: S=2r^2+2rhsolve for h.

Answer 1

Since the formula of the area of the cylinder is

`S=2\pi r^2+2\pi rh`

To solve for h we have to isolate h on one side and make its coefficient equal to 1

To do that, Subtract 2pi r^2 from both sides

`\begin{gathered} S-2\pi r^2=2\pi r^2-2\pi r^2+2\pi rh \\ \\ S-2\pi r^2=2\pi rh \end{gathered}`

Divide both sides by 2pi r

`\begin{gathered} (S-2\pi r^2)/(2\pi r)=(2\pi rh)/(2\pi r) \\ \\ (S-2\pi r^2)/(2\pi r)=h \end{gathered}`

Switch the 2 sides

`h=(S-2\pi r^2)/(2\pi r)`