Region S is bounded above by the horizontal line y=1 and below by the graph of y=lnx for 1≤x≤e. Region S is revolved about the horizontal line y=−3.
(a) For a fixed value of x in the interval [1,e], express the distances from the line y=−3 to (i) the line y=1 and (ii) the curve y=lnx. Clearly identify which distance corresponds to the outer edge and which corresponds to the inner edge of a representative circular cross-section.
(b) Write, but do not evaluate, a definite integral whose value is the exact volume of the solid obtained by revolving region S about the line y=−3.
(c) Use a calculator to approximate the volume of the solid to the nearest thousandth of a cubic unit.