The formula for the surface area A of a cylinder with radius r and height h is given. Solve for h.a = 2\pi {r}^(2) + 2\pi {r}h

Question

The formula for the surface area A of a cylinder with radius r and height h is given. Solve for h.
`a = 2\pi {r}^(2) + 2\pi {r}h`

Answer 1

The formula for the surface area A of a cylinder with radius r and height h is:

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

Solving for h:

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

The answer is h=(A/(2r*pi))-r