A solid is generated by revolving the region bounded above by and below by the -axis…
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A solid is generated by revolving the region bounded above by y=sinx+3 and below by the x-axis over the interval 0≤x≤π about the x-axis. A cylindrical hole of constant radius 2 is then drilled completely through the center of the solid along the x-axis, leaving a hollowed-out object.
(a) Explain why the remaining solid can be viewed as the accumulation of washers whose inner radius is constant and whose outer radius varies with x. State explicit expressions for both radii.
(b) Set up a definite integral that represents the volume of the hollowed-out solid.
(c) Evaluate the integral to find the exact volume, and simplify your final answer.