Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §8.3 Area of a Surface of Revolution, #13 · Calculus · Applications of integrals

By similar triangles … or

By similar triangles $R / s = R^{'} / s^{'}$ or $R s^{'} = R^{'} s$ . The middle radius $r$ is $\frac{1}{2} (R + R^{'})$ . Substitute for $r$ and $Δ s$ in the proposed area formula $2 π r Δ s$ , to show that this gives the correct area $π R s - π R^{'} s^{'}$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.3 Area of a Surface of Revolution, #13

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