Question

The formula for the surface area, S. of a cylinder, is S = 2xr? + 2xrh, where histhe height of the cylinder, and r is the radius of the base of the cylinder.

Answer 1

Formula for surface area of cylinder is:

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

We need to solve for h.

We take the term with h to one side and everything else to another, and solve:

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

Another simplified version:

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