Question

An energy drink container in the shape of a right circular cylinder must have a volume of 12 fluid ounces (1 fluid ounce is approximately 1.80469 cubic inches). The cost per square inch of constructing the top and bottom is twice the cost of constructing the lateral side. Find the dimensions that will minimize the cost. (Round your answers to two decimal places.)

v=pi*r^2*h=12(1.80469)=21.66
I got that r=1.20 but cant find h

Answer 1

r^2 h = 21.66/pi = 6.89

now you still have to do the problem

cost = cost of top and bottom + cost of side
x is cost of side metal per in^2

C = 2x pi r^2 + x (2 pi r h)
call c = C/2pix what we minimize
c = r^2 + r h
but we already know h = 6.89/r^2
c = r^2 + 6.89/r
luckily you know calculus so take dc/dr and set to 0
dc/dr = 0 = 2 r - 6.89/r^2
0 = 2 r^3 - 6.89
r^3 = 3.44