SOLUTION: A steel can in the shape of a right cylinder must be designed to hold 400 cubic centimeters of juice. It can be shown that the total surface area of the can (including the ends) is

Algebra ->  Surface-area -> SOLUTION: A steel can in the shape of a right cylinder must be designed to hold 400 cubic centimeters of juice. It can be shown that the total surface area of the can (including the ends) is      Log On


   

Question 875308: A steel can in the shape of a right cylinder must be designed to hold 400 cubic centimeters of juice. It can be shown that the total surface area of the can (including the ends) is given by S(r)=2 (pi)r^2+800/r, where r is the radius of the can in centimeters. (a) calculate S(2), S(3), S(4), and S(6), (b)From these values, determine the approximate length of the radius that minimizes the surface area.
(C) What does minimizing the surface area do for the company?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
S%28r%29=2%28pi%29r%5E2%2B800%2Fr

(a) Using pi=3.14 and rounding to 2 decimal places,
S%282%29=2%28pi%292%5E2%2B800%2F2=2%2A3.14%2A4%2B400=25.15%2B400=425.12
S%283%29=2%28pi%293%5E2%2B800%2F3=2%2A3.14%2A9%2B266.67=56.52%2B266.67=323.19
S%284%29=2%28pi%294%5E2%2B800%2F4=2%2A3.14%2A16%2B200=100.48%2B200=300.48
S%286%29=2%28pi%296%5E2%2B800%2F6=2%2A3.14%2A36%2B133.33=226.08%2B133.33=359.41

(b) The smallest S%28r%29+we+found+was+%7B%7B%7BS%284%29=300.48
so the radius that minimizes the surface area is approximately highlight%284cm%29 .

(c) The less surface area of metal used, the cheapest the can,
so minimizing the surface area reduces costs for the company.
That could lead to more profits.