If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Disc method: revolving around other axes

AP.CALC: CHA‑5 (EU), CHA‑5.C (LO), CHA‑5.C.2 (EK)
You might need: Calculator


Let R be the region enclosed by the line x, equals, 1, the line y, equals, 2, the line y, equals, 4, and the curve y, equals, left parenthesis, x, minus, 1, right parenthesis, squared.
A solid is generated by rotating R about the line x, equals, 1.
What is the volume of the solid?
Give an exact answer in terms of pi.