1. ## Linear Equation

Having a bit of trouble with this one. Can anyone help?

Many thanks.

Q.
The surface are, S, of a cylinder is given by S = 2 $\pi$r2 + 2 $\pi$rh. Its volume, V, is given by V = $\pi$r2h. Express V in terms of S & r only.

Attempt: V = S => $\pi$r2h = 2 $\pi$r2 + 2 $\pi$rh => $\pi$r2h = 2 $\pi$(r2 + rh) => V = ...

Ans.: V = $\frac{r}{2}$(S - 2 $\pi$r2)

2. ## Re: Linear Equation

$S=2\pi r^2 + 2\pi r h$
$\Rightarrow \pi r h = \frac{S}{2}-\pi r^2$

$\therefore V= \pi r^2 h = (\pi r h)r=\left( \frac{S}{2}-\pi r^2 \right)r= \boxed{\frac{r}{2}\left( {S}-2\pi r^2 \right)}$

3. ## Re: Linear Equation

Great. Thank you very much.

4. ## Re: Linear Equation

None of these equations are linear...