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

Question

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

Quizplus · Accepted Answer

The Shell Method is easier to apply in this case because the axis of rotation is vertical (the y-axis) and the solid has a horizontal cross-section. The shell method involves integrating the circumference of cylinders (shells) that are parallel to the axis of rotation and summing their volumes. Therefore, the Shell Method is the most convenient choice for finding the volume of the solid obtained by rotating the region in the figure about the y-axis.

To Compute the Volume of the Solid Obtained by Rotating