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Q&A How can you forebode that amount of wood in a napkin ring is the same, regardless of the size of the sphere used ?

1 answer · posted 4mo ago by Sunny‭ · edited 4mo ago by Sunny‭

Question intuition calculus

#3: Post edited by $user avatar$ Sunny‭ · 2024-06-20T18:14:44Z (4 months ago)

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Stewart, Clegg, Watson. *Calculus Early Transcendentals*, 2021, 9th edition. page 467. Problem 64.
![](https://i.imgur.com/6k9kHrx.jpeg)
When I attempted this question, I thought I miffed, because my answer lacked R and r! Even after seeing the solution, I still can’t intuit why the napkin ring’s volume is independent of R and r. Before attempting any paperwork, how can a student forefeel that the napkin ring’s volume shall be independent of R and r ?
![](https://i.imgur.com/a02inbr.jpeg)

Stewart, Clegg, Watson. *Calculus Early Transcendentals*, 2021, 9th edition. page 467. Problem 64.
![](https://i.imgur.com/6k9kHrx.jpeg)
When I attempted this question, I thought I flubbed, because my answer lacked R and r! Even after seeing the solution, I still can’t intuit why the napkin ring’s volume is independent of R and r. Before attempting any paperwork, how can a student forefeel that the napkin ring’s volume shall be independent of R and r ?
![](https://i.imgur.com/a02inbr.jpeg)

#2: Post edited by $user avatar$ trichoplax‭ · 2024-06-20T18:14:20Z (4 months ago)
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How can you forebode that amount of wood in a napkin ring is the same, regardless of the size of the sphere used ?

Stewart, Clegg, Watson. *Calculus Early Transcendentals*, 2021, 9th edition. page 467. Problem 64.

![](https://i.imgur.com/6k9kHrx.jpeg)

When I attempted this question, I thought I miffed, because my answer lacked R and r! Even after seeing the solution, I still can’t intuit why the napkin ring’s volume is independent of R and r. Before attempting any paperwork, how can a student forefeel that the napkin ring’s volume shall be independent of R and r ?

![](https://i.imgur.com/a02inbr.jpeg)

calculus

intuition calculus

#1: Initial revision by $user avatar$ Sunny‭ · 2024-06-20T12:25:06Z (4 months ago)

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How can you forebode that amount of wood in a napkin ring is the same, regardless of the size of the sphere used ?

Stewart, Clegg, Watson. *Calculus Early Transcendentals*, 2021, 9th edition. page 467. Problem 64.

![](https://i.imgur.com/6k9kHrx.jpeg)

When I attempted this question, I thought I miffed, because my answer lacked R and r! Even after seeing the solution, I still can’t intuit why the napkin ring’s volume is independent of R and r. Before attempting any paperwork, how can a student forefeel that the napkin ring’s volume shall be independent of R and r ?

![](https://i.imgur.com/a02inbr.jpeg)

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