Find the Volume of Cones using Integral Calculus

Hi friends! I will show you how to find the volume of cones by using integral calculus!
The formula for the volume of any shape is the definite integral from one end of the shape (let's call it "a") to the other end of the shape (let's call this "b"). So the integral is from a to b of the area of the cross-section (If you cut or slice the shape, you find the area of the open surface) and then dx. We are trying to find the volume of the cone.
Here, the area of the cross-section of the cone is the circle! The area of a circle is pi times the radius squared. From the figure shown of the cone, you can take the height of the cross-section "y" divided by the total height "h". Set this equal to the radius of the circle "x" divided by the total radius "r". This is the proportional ratio/fraction method. You solve x in terms of y to get the area of the cross-section and substitute it into the definite integral volume formula!
In the next video, I will show you how to find the volume of a square pyramid using integration.
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[@D0CTS]

Legend, I've just spent a solid couple of hours going through my math homework trying to figure it out until I came across your videos. They're simple, engaging, and you got the right voice for this stuff bro. Earned another sub.

[@QuocDatPhung]

Thanks Matthew! You can find all of my Calculus videos in this playlist here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA Please share with your fellow classmates if you find them helpful :)

[@D0CTS]

@@QuocDatPhung Thank you for the links and tutorials, I will absolutely share this with my classmates.

[@QuocDatPhung]

@@D0CTS Thank you so much Matthew! It means a lot to me :))

[@ggxsky4811]

I KINDA FIGURED IT BUT COULDN'T FIGURE OUT THE FUNCTION WITH RESPECT TO Y

[@BeauGeorge]

Very concise and understandable explanation. Even my 67 year old brain many years from my calculus lessons could comprehend it!

[@QuocDatPhung]

Thank you Beau George! I'm glad you like it! You can find the rest of my Calculus II videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@NinjaAdvisor]

Wow! Similar triangles help us solve the general formula of cones. I was overthinking it, was trying to find a relationship between the height and radius. Thanks appreciate it.

[@QuocDatPhung]

Thanks Ninja! You can find all of my Calculus videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA Please hit subscribe and share with your classmates! I hope this will help them too!

[@ggxsky4811]

Same problem lol

[@purifynature8479]

Easy to grasp the concepts.

[@QuocDatPhung]

I'm happy to hear that!

[@OMGITSMELOL]

thank you, i had been trying to figure out the volume of a circular pot with a smaller base than top and this explanation made it click

[@QuocDatPhung]

You're very welcome! You can find all of my Calculus II videos like this one here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@reyansh7823]

Sir can we take that y length from bottom of cone . Then ratio will be ( h-y)​/h = x/r @@QuocDatPhung

[@chriskattan]

Thank you for this clear explanation. I was having trouble understanding this concept in my homework.

[@QuocDatPhung]

You're very welcome! You can find the rest of my Calculus 2 videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@TheTigerBin]

Excellent work!

[@QuocDatPhung]

Many thanks!

[@kekiir]

best way to understand integrals!

[@QuocDatPhung]

Thanks Kekkir! Please kindly subscribe xd you can find all of my Calculus II videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@HimanshuKumar-zf1ql]

What a beautiful explaination!! मजा आ गया

[@QuocDatPhung]

omg I'm so happy to hear that! If you really like it, don't forget to let your classmates know about this video too! Please consider subscribing! It means a lot!

[@muharremyusufzorluer5150]

thank you bro it was a really helpful to understand the logic of volume

[@QuocDatPhung]

Thank you Muharrem! Please support my channel by subscribing!

[@shang0794]

This is the easiest tutorial that I have watched! Tomorrow is my report, wish me luck!😖

[@QuocDatPhung]

Thank you! And good luck too! You got this!

[@shloktate9491]

Thanks bro!! From India

[@QuocDatPhung]

You're welcome Shloktate!! I'm really glad you enjoyed my video! I would really appreciate if you could share with your classmates or kindly subscribe ~ you can find all of my Calculus II videos in this link: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@Dragon-hk2wu]

Thank you!

[@QuocDatPhung]

Welcome!

[@thitamhieple9818]

This is awesome!

[@QuocDatPhung]

:)

[@AshvinKaththamuthu-te1pb]

TYSM it’s very understandable !

[@QuocDatPhung]

Haha thank you! Don't forget to share with your classmates and kindly subscribe ~ you can find all of my Calculus II videos in this link: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@henryubah5031]

Your videos are amazing bro

[@christiaan3315]

Wonderful. Thank you!

[@QuocDatPhung]

You're very welcome Christiaan! Please kindly subscribe! You can find all of my Calculus II videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@crypto_geo7533]

Very Helpful!

[@QuocDatPhung]

Thank you George!

[@dineshkumthekar3135]

Great..so simple

[@QuocDatPhung]

Thank you very much! You can find the rest of my Calculus II videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@Mramanofficial07]

Thanks bro❤❤🙏🙏

[@QuocDatPhung]

Thank you Mr.Aman! I'm glad you enjoyed my video! I would really appreciate if you could share with your classmates or kindly subscribe ~ you can find all of my Calculus II videos in this link: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@Mramanofficial07]

@@QuocDatPhung bro you are amazing I subscribe your channel 🙏🙏

[@QuocDatPhung]

@@Mramanofficial07 That's awesome! Thanks so much! :)))

[@sa.kh.]

i loved you 😎🔥👍 from palestine

[@QuocDatPhung]

Thank you Yasir! Please don't forget to support me by subscribing and sharing my Calculus videos with your classmates!

[@sa.kh.]

@@QuocDatPhung anytime ❤️✌️

[@joelnamabwaza3896]

Amazing brother

[@QuocDatPhung]

Thank you Joel! If you want to see more of my Calculus videos, you can find all of them inside this link: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@mathfoundation8588]

you are just brilliant

[@QuocDatPhung]

Thank you! Please kindly subscribe if you wanna buy me coffee for free and share with your classmates to help them too!

[@dreamhunterskingdanger292]

Excellent

[@QuocDatPhung]

Thanks so much DreamHunter! If you like my Calculus videos, you can find all of them here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@zachwallace483]

earned a like and sub from this video

[@QuocDatPhung]

Thank you very much Zach! You can find all of my Calculus videos here: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@Noname-wu3wj]

Super bro

[@QuocDatPhung]

Thanks Noname! Don't forget to share with your classmates and kindly subscribe ~ you can find all of my Calculus II videos in this link: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@kaziabdullah9565]

She can we do the integral in perspective of x not y pls let me know it .

[@quocdatphunggaming9921]

Yes, we can integrate in terms of x instead of y. But the way I'm showing you is the easiest. Being able to integrate with respect to y allows you to solve some problems very easily in the future.

[@QuocDatPhung]

Let me know if that makes sense.

[@kaziabdullah9565]

Oh thanks brother , I tried that with respect to X but that seems more deficult to me

[@QuocDatPhung]

@@kaziabdullah9565 That's right :) I always choose the easiest methods to show on my videos. They might seem strange at first, but trust me, it's the easiest. There's a calculus video I made where you have to integrate with the positive direction of the y axis pointed downwards, but there's a reason to that, because if you do it with the positive direction pointed upwards, it is way more difficult :)

[@kaziabdullah9565]

Bro I think then you can also make a video on that x Axis than we can easyly compare it to the easiest one and have clear cut concept

[@omamori8930]

thx king

[@QuocDatPhung]

Thanks Omamori! You can find the rest of my Calculus videos in this playlist: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA As well, don't forget to subscribe and share! I'd really appreciate it!

[@poisedperson6475]

If you aren't a teacher, I don't blame you, but you'd be a good one 😅

[@QuocDatPhung]

Thank you Poised! Please kindly share and subscribe (it means a lot) you can find all of my Calculus II videos in this link: kzbin.info/aero/PLeTO6OT3-FKmuCeO97iKt_Aibx-a938JA

[@martinmaslein4758]

chinardopete