Problem

Solve Example 9 taking cross-sections to be paral…

02:07

Problem 63 Hard Difficulty

(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.

Answer

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

Topics

Applications of Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 2

Volumes

Discussion

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Watch More Solved Questions in Chapter 6

Problem 1

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Video Transcript

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Topics

Applications of Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 2

Volumes

Top Calculus 2 / BC Educators

GH

Grace H.

Numerade Educator

Heather Z.

Oregon State University

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor