surface area/volume of cylinder

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• December 1st 2010, 06:10 AM
Joker37
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.

Anyway if anybody could please help me with this question I will be eternally grateful!(Nod)
• December 1st 2010, 06:27 AM
e^(i*pi)
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
• December 1st 2010, 08:13 PM
Joker37
$V=\pi r^2h$

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

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