# Math Help - surface area/volume of cylinder

1. ## surface area/volume of cylinder

The volume of a solid cylinder is $128\pi cm^{3}$.
Show that the total surface area, $A cm^{2}$, is $A=2\pi r^{2}+\frac{256\pi}{r}$ where r>0.

2. Volume of a cylinder: $V = \pi r^2 h$

Surface area of a cylinder: $A = 2\pi r^2 + 2\pi r h$

================================================== =========================

In your case: $V = \pi r^2h = 128\pi$

Rearrange to make $h$ the subject (because it will need to be eliminated): $h = \dfrac{128}{r^2}$

Sub the above expression for h into the equation for A at the top of the post and simplify

3. $V=\pi r^2h$

$h=\frac{128}{\pi r^2}=\frac{128}{r^2}$

$A=2\pi r^2 +2\pi rh$
$=2\pi r^2 +2\pi r(\frac{128}{r^2})$
$A = 2\pi r^2+\frac{256\pi}{r}$