surface area/volume of cylinder

**Joker37** · December 1st 2010, 06:10 AM

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.

Anyway if anybody could please help me with this question I will be eternally grateful!

**e^(i*pi)** · December 1st 2010, 06:27 AM

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

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

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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