Calculus 1: Max-Min Problems (23 of 30) Maximum Right Circular Cone

In this video I will find the maximum volume of a cone that can be constructed from a circle of radius R and the angle of the cut-out of the circle.

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[fcccrlsn]

So is it correct to say that....theta will always be 66 degrees ..no matter what the initial big R value is ?    (In regards to finding Max Vol of cone.)

[holretz]

It's very nice. Afterwards one could ask students about continuity of V(h), and if V'(h) is defined everywhere in the optimization interval. Also the values at the endpoint should be checked.

[intekhabalam]

Professor, why couldn't we use the equation, " S = R* (theta) " where S is the length of the arc which is basically " 2 * Pi * r " and then from that figure out "theta" ? Why am I getting a different result from this method from your method to figure out "theta" ?

[kevincooper]

could you explain biasing of a transistor, why need to bias it ? what are the formulas used for biasing a transistor and also does it add dc signal voltage with ac signal to amplify ac input by its current gain factor alpha ?

[Sam]

Very nice explanation thx. How to calculate V(max) with teta ? What will be the expression of V(max) with teta ? Thank you 👍🏽

[fcccrlsn]

I  tried it with different  values of  big R and the value of little r as well as value of height ..h..changes .... hence the value of angle theta will also vary. Pls  ignore my previous comment about a  66 degree constant theta.

[audreyc]

Amazing video and explanation! THANK YOU!!!!

[calebfoxschool]

Such an amazing explanation, thank you so much

[salmanabdulhakimsah]

thank you, sir, it's be so easy and fun

[fcccrlsn]

You are  a gifted professor.I think this prob would be easier for us to follow if you initially assigned a numerical value to Big R .  Do you agree?

[callumhamilton]

Does anyone know how to verify that this is a maximum using derivatives?

[josephvanderpool]

You’re making one mistake at the end which is giving you the wrong answer, when you say what the circumference is equal to, but I will say this method is easier than taking a derivative of the entire volume equation with respect to theta. The answer should be pi(⅔)^(½), if you just say (R)theta=2pi(r)

[koik]

I LOVE YOU I LOVE YOU I LOVE YOU I LOVE YOU I LOVE YOU I LOVE YOU I LOVE YOU I LOVE YOU

[tanzidahmed]

What is the need of the angle sir??i didnt get it

[HardikKundalwal]

but where is the calculus I mean differentiation?