Question 6

The volume of a cylindrical can of radius r and height h is given by V (r, h) = r2h.

(a). Find the differential dV in terms of dr and dh.

(b). A cylindrical can is measured to have height 8 centimeters and radius 5 centimeters, with an error of at most 0.1 cm in these measurements. Use differentials to estimate the maximal error in measuring the volume of the can.

(c). Which affects the error in the volume more: the error in the radius, or the error in the height?