Posted by **Josh** on Friday, November 9, 2007 at 8:07pm.

Q)

'What are the dimensions of a cylinder that has the same maximum volume as the box (1131.97 cm2), but uses the minimum amount of material to make it?'

Here are the notes I have so far:

SA=2Pi r^2 + 2 Pi r (1131.97/Pi r^2)

Now i need to use derivatives, I don't know how!

SA1=

Then these notes-

at min. gradent =0 therefore SA1=0

rearrange to find r

sub r in to find

Anyone have any clue? thanks. its my assinment

- Math -
**Reiny**, Friday, November 9, 2007 at 10:45pm
your line

SA=2Pi r^2 + 2 Pi r (1131.97/Pi r^2)

reduces to

SA=2Pi r^2 + 2263.94/r

then

SA' = 4(pi)r - 2263.94/r^2

now set this equal to zero for a minimum surface area, so....do the algebra

r^3 = 2263.94/(4pi)

= 180.15862

take the cube root to get r,

go back into 1131.97/(Pi r^2) to get the height

(I got h = 11.296 and r = 5.648

notice that would make the diameter equal to the height, mmmmhhhh?

isn't Calculus wonderful???)

- Math -
**Josh**, Saturday, November 10, 2007 at 12:09am
you couldn't show all the working could you? its just that i don't understand how to do them, and can't do them

thanks

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