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Volumes of Revolution
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Finding the volume of a solid revolved around a function or axis to create a 3D figure
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Volume of revolution about x-axis
AHL AI 5.12
A curve y=f(x) can be revolved around the x-axis to produce a 3D solid. The following example shows y=2+sinx revolved 2π about the x-axis.
The volume of the resulting solid is given by
V=∫abπy2dx📖
Volume of revolution about y-axis
AHL AI 5.12
The volume of the solid produced by revolving a curve 2π about the y-axis by finding x in terms of y and evaluating
V=∫abπx2dy📖
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