Here we consider various solids of revolution whose aris is the diagonal line y=x. The goal is to adapt the "pile of thin disks" idea from Question 2(b) to this new situation. For each real constant m
≠ 1, the curve y=mx+(1−m)x² is a parabola that crosses the line y=x at the points (0,0) and (1,1). Let R(m) denote the finite region between the parabola and the line. Then let S(m) denote the solid generated by rotating R(m) around the line y=x. We are interested in the volume of the solid S(m) : call this volume V(m). Using the same set of axes, draw the line y=x and several of the parabolas y=mx+(1−m)x². Your sketch should show enough parabolas to communicate all the different types of possible shapes.