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