Question

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

Answer 1

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???)

Answer 2

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