Optimization: Find Cylinder With Largest Volume Inscribed in a Sphere

This video shows how to find a right circular cylinder with largest volume that can be inscribed in a sphere of radius r.

[@GetupandRise]

Amazing! you made it very lucid and elucidated it brilliantly.

[@crowsmathclass]

Thank you. Glad it helped.

[@karizamakanty2813]

Thank you, you do it very quickly and briliant!

[@crowsmathclass]

Thank you. Glad it helped.

[@aranduslarson1438]

this helped so much thank you!

[@crowsmathclass]

You’re welcome. Glad it helped.

[@saladassgaming7514]

Omg your solution is simple than my book's explained solution ! Thank you 😄

[@crowsmathclass]

You’re welcome. Glad it helped.

[@AryanTiwari-c1v]

Bahut acche se samj me aya❤

[@CTMUSINGULARITY]

Thank you so much! Very helpful. God bless. 🙌💫

[@crowsmathclass]

You’re welcome.

[@yikes6873]

Thank you so much! This helped out a lot!

[@crowsmathclass]

You’re welcome.

[@DereckGeorge]

Helped me a lot. Thanks

[@crowsmathclass]

You’re welcome.

[@wenxiwu3542]

Why do you set the prime equation to 0?

[@crowsmathclass]

You set the derivative equal to zero. This gives you you’re critical numbers. This is how you find your max and min values.

[@wenxiwu3542]

@@crowsmathclass Thank you very much! Now I understood.

[@alvinjarolimek2747]

Thanks, that is so interesting

[@crowsmathclass]

You’re welcome.

[@huntertv1352]

Please give some example problem

[@crowsmathclass]

You can search my channel for optimization and find a lot more examples.

[@cece8309]

thank you sir

[@crowsmathclass]

You’re welcome.

[@MariaGarcia-uc6te]

thank you!

[@crowsmathclass]

You’re welcome.

[@tadesebirke4397]

v.good

[@crowsmathclass]

Thank you.

[@amber1171]

Amazing

[@crowsmathclass]

Thank you.

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[@Maya-xs9xn]

Excellent explanation. Thank you very much.

[@crowsmathclass]

Thank you.

[@JAGhost1502]

I put this as the answer but somehow its saying that its wrong

[@jotatrujillo5984]

Why u don't take the derrivate of the radius?

[@crowsmathclass]

r is considered a constant.

[@BrownOpsLeak]

playback speed =2x, you're welcome

[@abdullahalshake5750]

Thanks

[@wynnedalaneydecastro2754]

what would be the least possible volume?? In exact numbers?

[@fortun8diamond]

Thanks for this. I saw this problem today in my practice questions. Didn't know what to do because this was me looking for V in terms of r.

[@crowsmathclass]

You’re welcome.

[@christianmiguelcubilla5090]

why x disappeared at 5:13?

[@Zekaz_Nohea]

Thank you very much for making this, this was extremely helpful.

[@crowsmathclass]

You’re welcome. Glad it helped.

[@bitlystarly7757]

Haist ,

[@simbiraimunashelmberi7702]

thank you very helpful, but I have a question, Why did we differentiate the volume equation and equated the differential to 0

[@crowsmathclass]

You’re welcome. Glad it helped. This gives you the critical values. This is how you find max and min values. You probably recall this from graphing.

[@simbiraimunashelmberi7702]

@@crowsmathclass oww yah true..thank you for the clarity

[@Mr_deepak708]

Thanks so much 😊

[@crowsmathclass]

You’re welcome.

[@ChefFarisMom3]

Thanks a lot❤

[@crowsmathclass]

You’re welcome.

[@ericyarmey4454]

Thanks you saved me before my math test

[@crowsmathclass]

You’re welcome. Good luck on your exam.

[@miaflynn3678]

This helped me SO MUCH thank you!!

[@crowsmathclass]

You’re welcome. Glad it helped.

[@williamlefebvre2236]

I always overthink this! Thank you Steve!

[@crowsmathclass]

You’re welcome.

[@jhericadulosa5852]

Thank you

[@crowsmathclass]

You’re welcome.

[@richardma3932]

Very useful

[@crowsmathclass]

Thank you.

[@bishopvillagran7801]

Nice video really helped!

[@crowsmathclass]

Thank you. Glad it helped.