SOLUTION: A container is designed in the shape of an open right circular cylinder (bottom but no top). The container is to hold 1248 cc. The base must be cut from the smallest square piece o
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Question 1028529: A container is designed in the shape of an open right circular cylinder (bottom but no top). The container is to hold 1248 cc. The base must be cut from the smallest square piece of material and the corners of this piece are then wasted. Assume no other materials need be wasted in construction. Find the height of the container for which the cost of the material used to create it is the minimum possible. Express your answer as a decimal rounded to the nearest hundredth.
Answer: 8.64
So I know it is a rather easy problem given that I must just find the dimesnions. However, I am asked to find the height of the container that would result in the MINIMUM cost/use of material. How do I find the minimum?
Any help is greatly appreciated!! Thank you in advance! Answer by mananth(16946) (Show Source):
h= 1248/pi r^2
side of square will be 2r where r is the radius of cylinder.
Area of base = 4r^2
Total surface area = 4r^2 + 2*pi*r*h
=4r^2 + 2*pi*r*(1248/r^2)
= 4r^2 +2496/r
For minimum area take the derivate dA/dr
dA/dr =8r-2496/r^2
0 = 8r-2496/r^2
8r=2496/r^2
8r^3=2496
r^3=312
r=6.78
V= 1248 = pi*r^2*h
1248/(pi*(6.78)^2)=h
h=8.64 cm
m.ananth@hotmail.ca
