A manufacturer wishes to create a plug whose shape is obtained by revolving the…
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A manufacturer wishes to create a plug whose shape is obtained by revolving the region bounded by the graph of y=x, the x-axis, and the vertical line x=a about the x-axis. The plug must displace exactly 518π cubic centimeters of water.
(a) Write, but do not evaluate, a definite integral representing the volume of the plug in terms of the unknown upper limit a.
(b) Determine the exact value of a that yields the required volume. Show all steps leading to your result.
(c) State the units of your answer in part (b) and interpret what the value of a represents in the physical context of the plug.