(a) Set up an integral for the volume of a solid torus (the donut-shaped solid shown in the figure) with radii $ r $ and $ R $.

(b) By interpreting the integral as an area, find the volume of the torus.

a) 8$\pi R \int_{0}^{r} \sqrt{r^{2}-y^{2}} d y$

b) $V=2 \pi^{2} r^{2} R$

Applications of Integration

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Numerade Educator

Oregon State University

Baylor University

University of Michigan - Ann Arbor

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