let the radius be r
and let the height be h
πr^2 h = 2000π
h = 2000/r^2
we want to minimize the surface area A
A = 2πr^2 + 2πrh
= 2πr^2 + 2πr(2000/r^2)
= 2πr^2 + 4000π/r
dA/dr = 4πr - 4000π/r^2
= 0 for a minimum of A
4πr = 4000π/r^2
r = 1000/r^2
r^3 = 1000
r = 10
then h = 2000/100 = 20
the height should be 20 inches, and the radius should be 10 inches.
Notice the height = diameter for a minimum surface area of a cylinder.
(Thank you for any help because I am not good at setting up word problems)
What are the dimensions that will minimize the amount of material needed to manufacture a standard oil drum that is in the shape of a cylinder, with closed top and bottom. The drum must have a volume of 2000pi cubic inches. (Again thank you for any help)
1 answer
1 answer