Cylindrical Shells to Find the Volume of Solids of Revolution | Calculus 2

What is the cylindrical shell method to find the volume of solids of revolution? That's exactly what I'm going to talk about today. The cylindrical shell method says that if your solid of revolution looks like a mountain with a dent inside it, then use the cylindrical shell method. Super easy. It really helps with finding the volume.
A shell is an empty cylinder with no top and bottom lid. So what's the surface area of a shell? Well, the surface area is the same as the circumference times the height. The circumference will be 2pi times radius, and the height is f(x) since that is the y value of the function.
Whereas if your solid of revolution looks like a cucumber cut in half (shown in the previous video), then you use the dishwasher method. If your solid of revolution does not look like a cucumber cut in half, then you use the cylindrical shell method. I did three examples using the cylindrical shell method to find the volume in the video.
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[@kudakwashemcmillengomba603]

I like how this guy smiles. He really enjoys this. Once wrote a test and passed because of him, it's a few hours bfre my exam....ik I'm going to do well...Keep up the good work!!!

[@QuocDatPhung]

Hi Kudak! Thanks so much for your kind words :) I hope you did well on your exams! If you still need help with Calculus II, you can find all of my videos in this link here: czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@StubbornSunBurn]

TYVM, i was lost about when to use the disk washer and cylindrical methods, but you just explained everything.

[@QuocDatPhung]

I'm glad it helped Antoni! Please kindly subscribe and you can find the rest of my Calculus II videos in this playlist: czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@xi421ruizhidavin5]

thankful, i really enjoy your explanation

[@QuocDatPhung]

Thanks so much Davin! If you found it helpful please do smash that subscribe button and share with your classmates! Also, you can find the rest of my Calculus videos in this playlist: czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@user-ry3eo7qk5c]

bro thank you , you help me a lot

[@QuocDatPhung]

You're very welcome! You can find all of my Calculus II videos here: czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@Idraw1010]

Nice video, very well explained. 👍

[@QuocDatPhung]

Thank you so much! Please subscribe and share with classmates; it means a lot!

[@imjohn8843]

thank you, you helped me a lot with the practice questions

[@QuocDatPhung]

You're welcome John! You can find all of my Calculus II videos in the following link (don't forget to share and kindly subscribe!): czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@user-bh9rw8ij8v]

tysm for this video too. from south korea.

[@QuocDatPhung]

You're very welcome! Please kindly subscribe and share with your friends my Calculus playlist: czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@aryamore7416]

Thanks man!

[@QuocDatPhung]

You're so welcome Arya! Please kindly subscribe! You can also find the rest of my Calculus 2 videos here: czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html

[@a.m2132]

Hey super cool to see a fellow Ottawa u student ! Your great at what you do thanks!

[@QuocDatPhung]

Thanks a lot! Did you know, the youtuber Tech With Tim also went to Uottawa? He has more than a million subs xd

[@a.m2132]

Oh wow I had no idea, that's amazing! you'll get there soon! @@QuocDatPhung

[@siyabongamdluli1946]

This is excellent explanations, thank you

[@QuocDatPhung]

Thanks so much Siyabonga! You can find the rest of my Calculus videos in the link below, and don't forget to subscribe and share with your classmates! czcams.com/play/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA.html