Volume of cap of sphere

In this quick calculus video I calculate the volume of the cap of height h of a sphere of radius r using the disk method from calculus.
Catherine Michalska : I’ve been working on this problem for two hours now, and you did it in less than 15 min. Thank you so much!
Leonard Romano : Another marvelous method would be to assume a cubic polynomial in h and then take 4 values that you now and just do the algebra (h=0, h=r are trivial, just take h=r/2 and maybe h= 3/4 r) and you will get to the same result. The values for the Volume at the different values of h you would derive with elementary geometry. If you did that you would not need to calculate any Integrals.
Edit: would also work for higher dimensional spheres.
Matthew Zárate : How interesting, I was working on this problem in my calc book two nights ago! It was at the end of chapter 6 in my Stewart Calculus textbook.
Yan Banales-Garcia : Really nice video, you are an absolute legend!
Alejandro Veliz : Thank you so much, I'm a college student from Guatemala, and this video really help me to undertand how to operate the integral of a volume

Volume of a Sphere Cap


mushroom1212 : I have a question - I'm trying to solve this with R=5, h=3 and r=sqrt(21)
When integrating I'm getting 63pi, but when I use your final formula I get 36pi, which is the correct answer. Why is this, or what am I doing wrong? Thanks.
TheRye : Thank you!

Crypto Terms 101: Basics (Volume , Market Cap , Supply) and more

In this episode I explain some basic cryptocurrency terms (volume, market cap, and supply) everyone should know as well as how to apply these terms when looking at new cryptocurrencies. I also discuss how to relate coins by looking at volume, market cap and supply.

Links: https://coinmarketcap.com/

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If you want to donate to the addresses below to support me and the channel it would be appreciated:

BTC: 1A4obN8bRNfUVynk5YFb1aY4BRPLBYiSJt
ETH: 0xca2942efc2aba55c18dfa4a74977be0a2f60cd8b
LTC: Ldr7kEF9B7c52qiygJQghv8Gd7qk7Kc3bZ
ARK: APjESUbCJbmsPC33Y5BP1FwyRK2KiGmzwu

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To get started buying crypto currencies, use the link below to get $10 of free bitcoin credited to your first purchase of $100 or more:

https://www.coinbase.com/join/593b3ab1f59a440a668b2719

****Disclaimer****

I am not a financial advisor and all content on this channel should be regarded as my opinion and viewpoints. Always do your own research before interacting with crypto currency in any potential.

Background music:https://www.bensound.com
Chris Mo : Exceptionally helpful. Most of these are just people looking to flex their terminology. Thanks for keeping it simple.
TheRottenBone : Great video! Helped me a lot! keep creating more of these!really useful thank you!
Mike Massey : Very helpful, learned some new terms and some topics to research! Great video!
Turnitaround : Hi, so can a currency just increase the total supply of a coin at will? Or once it's set, it's set? Thanks
Andrew Murphy : This is beautifully explained. Ive watched several videos to try to understand market cap better and this is the one that does the best job of it. I also love the relaxed style in which you explain things. More please :)

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