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 cylindrical silo set on a concrete block has inside diameter 12 ft and height 80 ft without the lid. If the silo’s lid and curved walls are 6 in and 4 in thick, respectively, use calculus to estimate the volume of the material used for the silo.