To compute the volume of the solid obtained by rotating the region shown in the figure about the y-axis, the most convenient method is
A) the Disk Method.
B) the Disk Method in addition to the Shell Method.
C) the Shell Method.
D) Integration by Parts.
E) none of these methods.

Question

To compute the volume of the solid obtained by rotating the region shown in the figure about the y-axis, the most convenient method is 
A) the Disk Method. 
B) the Disk Method in addition to the Shell Method. 
C) the Shell Method. 
D) Integration by Parts. 
E) none of these methods.

Quizplus · Accepted Answer

The solid is best rotated using the Shell Method because the axis of rotation is vertical and the area being revolved around the y-axis is horizontal. To use the Disk Method, we would need to slice the region vertically and integrate along the x-axis, which would result in more complicated integrals. Adding the Disk Method to the Shell Method would be unnecessary and possibly confusing for this problem. Integration by Parts is not applicable for finding the volume of a solid of revolution.

To Compute the Volume of the Solid Obtained by Rotating