Optimization Calculus Problems Volume Calculus 1 AB

Maximizing Volume of Cube w/fixed Surface Area 1:53
Maximizing Volume of Cone Inscribed in a Sphere 11:51

Optimization Calculus Problems Minimizing Lengths
Optimization Cylinder in Sphere with Radius r

[reganbowman]

This was AWESOME. It was almost the exact same problem that my teacher gave me for homework tonight. Thank you!!!

[profrobbob]

The volume is calculated by combining two figures, the cylinder between the two hemispheres pi*r^2*h and the sphere 4/3*pi*r^3. The cost per square unit of material is 4 times as much for the hemispheres 4k, than the cylindrical side k. So if the metal for the cylinder costs 50 dollars a square foot, then the end caps will cost 200 dollars a square foot.

[phillipkim]

At 32:57, if you were to find the first derivative, wouldn't c prime r equal to 2k(40/3 pi r + 5500/r^2) + 2(20pi r^2 + 5500/r) by the Product Rule?
I was really confused because you just only wrote 2k times the derivative of the inside at 33:59
If you could answer this question, thank you.

[curtislumber]

These are some great examples, but I'm having trouble with some more complex problems. Like the maximum value of the dimensions of a sheet of metal made into a gutter, and the maximum values of an open box (no top). 

[MrNgaiming]

Hi.

How does u get the 5500 = pie . r^2 .h + 4/3 pie . r^2 ??. if u're talking about the volume how come we need to add the pie . r^2 .h ?

Furthermore, why does the cost of the 2 pie. r .h. is multiply by only k and not 4k ?

Thanks so much and i like your videos

[MultiPenguin]

5:53
You're plugging in Y, but you wrote V(x).
Can you explain why the volume is written as V(x) and not V(y)?

[justineeakins]

How does he draw such a perfect sphere/cone diagram?? I imagine it goes something like that crazy Spongebob episode where he drives Squidward crazy in his art lessons....

[MrGittle]

Isn't it also possible for the height of the cone to be 10-h?.  Is this taken into account? 

[MrExtremehustler]

The picture is wrong. The square side is x*x. The longer side should by y. The equations however, are correct and that's what really matters. (for the first problem)