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:

$\begin{gathered} A=2\pi r^2+2\pi rh \\ \Rightarrow A-2\pi r^2=2\pi rh \\ \Rightarrow\frac{A-2\pi r^2}{2\pi r}=h \\ \Rightarrow h=\frac{A}{2\pi r}-r \end{gathered}$

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