Question

a company manufactures large cylindrical drums.the bottom and sides are made from a metal that costs $4.00 a square foot, while the reinforced lid costs $6.00 a square foot. ind thedmensions ofa drm that hasa volume of 10cubic feet and minizes the total cost

Answer 1

i mean find the dmensions of a drum that has a volume of 10 cubic feet and minizes the total cost

Answer 2

let the radius be r ft and the height h ft
πr^2h = 10
h = 10/(πr^2)

cost = 6πr^2 + 4πr^2 + 4(2πrh)
= 10πr§2 + 8πr(10/(πr^2))
= 10πr^2 + 80/r
d(cost)/dr = 20πr - 80/r^2 = 0 for max/min of cost

I got r = appr. 1.084 , h = 2.71