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A volume of revolution is the solid formed when a curve is rotated 360° about an axis. This topic uses V = π∫y² dx and V = π∫x² dy to calculate such volumes, including regions between curves. It appears across A-Level and iAL Pure Maths with the major exam boards. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
For rotation about the x-axis, integrate pi times y squared between the limits. Square the function before integrating, not after. For rotation about the y-axis, rearrange to get x in terms of y and integrate pi times x squared instead.
Before you start
It assumes you can handle definite integration and areas. Examined in Pure 4. You will lean on this again for modelling solids. The topic sits within Integration.
What you learn
The course works through the volume formula, squaring the curve, trig curves & double-angle and region between two curves. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Volumes of Revolution is a Integration topic in the A-level syllabus, covered here at the second year of A-level. There are 5 teaching sections and 5 fully worked examples, plus 5 sets of check questions. Related topics students usually take next include Area Between Two Curves, Area Under a Curve and Definite Integrals. For unlimited practice, the Integration revision engine builds new questions on demand and records your accuracy.
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