The surface area of the cylinder aluminum can is the measure of how much aluminum can needs. If can has radius r and height h, its surface area A and its volume V are provided by equations:
A= 2πr^2 + 2πrh and V=πr^2h
a) Volume V of the 12 oz cola can is 355 cm^3. Cola can is roughly cylindrical. State its surface area A as the funtion of its radius r, where r is measured in centimeters.
b) Graph A = s(r) surface area of the cola can whose volume is 355 cm^3, for 0 r 10.
c) Find domain of s(r)? Based on the graph, what, approximately, is range of s(r)?
d) Producers want to use least amount of aluminum (in cm^2) essential to make the 12 oz cola can. Use the answer in (c) to determine minimum amount of aluminum required. Express values of r and h which minimize amount of aluminum used.
e) Radius of the real 12 oz cola can is about 3.25 cm. Illustrate that real cola cans use more aluminum than essential to hold 12 oz of cola. Why do you believe real cola cans ar made to this way?