# surface area/volume of cylinder

• Dec 1st 2010, 06:10 AM
Joker37
surface area/volume of cylinder
The volume of a solid cylinder is $\displaystyle 128\pi cm^{3}$.
Show that the total surface area, $\displaystyle A cm^{2}$, is $\displaystyle A=2\pi r^{2}+\frac{256\pi}{r}$ where r>0.

• Dec 1st 2010, 06:27 AM
e^(i*pi)
Volume of a cylinder: $\displaystyle V = \pi r^2 h$

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

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

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

Sub the above expression for h into the equation for A at the top of the post and simplify
• Dec 1st 2010, 08:13 PM
Joker37
$\displaystyle V=\pi r^2h$

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

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