Each of Exercises 81 through 85 involves either the chain rule for partial derivatives or the incremental approximation formula for functions of two variables.

A soft drink can is H centimeters (cm) tall and has a radius of R cm. The cost of material in the can is 0.0005 cents per cm², and the soda itself costs 0.001 cents per cm³.

a. Find a function C(R, H) for the cost of the materials and contents of a can of soda.

b. The cans are currently 12 cm tall and have a radius of 3 cm. Use calculus to estimate the effect on cost of increasing the radius by 0.3 cm and decreasing the height by 0.2 cm.