Question
Find the surface area of the torus obtained by rotating the circle$x^{2}+(y-b)^{2}=r^{2}$ about the $x$ -axis (Figure 17$) .$
Step 1
We have $x^{2}+(y-b)^{2}=r^{2}$, so $x^{2}+y^{2}-2by+b^{2}=r^{2}$. Rearranging, we get $x^{2}+y^{2}=r^{2}+2by-b^{2}$. Show more…
Show all steps
Your feedback will help us improve your experience
Xiaomeng Zhang and 61 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find the surface area of the torus obtained by rotating the circle $x^{2}+(y-b)^{2}=r^{2}$ about the $x$ -axis.
Find the surface area of the torus obtained by rotating the circle $x^{2}+(y-b)^{2}=r^{2}$ about the $x$ -axis (Figure 20$)$ .
FURTHER APPLICATIONS OF THE INTEGAL AND TAYLOR POLYNOMIALS
Arc Length and Surface Area
Surface Area The region bounded by $(x-2)^{2}+y^{2}=1$ is revolved about the $y$ -axis to form a torus. Find the surface area of the torus.
Integration Techniques, L'Hopital's Rule, and Improper Integrals
Improper Integrals
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD