For a closed cylinder with radius r cm and height h cm, find the dimensions giving the minimum surface area, given that the volume is 40 cm3.

Give exact answers...

So V=pi * r^2 * h

and A=pi * r * (2h+r)

and so i set them like this?

40 = pi * r^2 * h

am i doing this correctly so far?

Question

For a closed cylinder with radius r cm and height h cm, find the dimensions giving the minimum surface area, given that the volume is 40 cm3.

Give exact answers...

So V=pi * r^2 * h

and A=pi * r * (2h+r)

and so i set them like this?

40 =  pi * r^2 * h

am i doing this correctly so far?

phi · Answer

it looks like your area has only the bottom  = $ \pi r^2 $
you also want the area of the top.

anonymous · Answer

ohh so A= 2πr^2 * (2h+r) ?

phi · Answer

you will want to solve for h or r using 40 =  pi * r^2 * h
and use that in 
A= 2 pi r (h+r)

then set the derivative of A = 0

phi · Answer

http://math.about.com/od/formulas/ss/surfaceareavol_3.htm

anonymous · Answer

okay

so h= 40/ pi r^2 

?

so A = 2 pi r (40/pi r^2  +  r ) ?

anonymous · Answer

oh yay it's working again!!

anonymous · Answer

so is that right @phi ? h = 40/ πr^2 ?

agent0smith · Answer

This is the exact same thing as the last question, except the volume is 40 cm^3 instead of 8 cm^3

agent0smith · Answer

http://openstudy.com/study#/updates/5345b645e4b0ad0f64ad8a23

anonymous · Answer

yeah :/ so confusing!! 

 but i figured it out :)

yay!!