Can someone please help me with this question???

Determine the dimensions of the cone of maximum volume that can be inscribed in a sphere with radius 3?

- Oct 31st 2006, 01:55 PMphilipsach1Using the Derivative to Analyze Polynomial Function Model Problems
Can someone please help me with this question???

*Determine the dimensions of the cone of maximum volume that can be inscribed in a sphere with radius 3?* - Oct 31st 2006, 02:53 PMSoroban
Hello, philipsach1!

Did you make a sketch?

Quote:

[I] Determine the dimensions of the cone of maximum volume

that can be inscribed in a sphere with radius 3?

Code:`A`

* * *

* /:\ *

* / : \ *

* / : \ *

/ :3 \

* / : \ *

* / O* \ *

* / 3* : *3 \ *

/ * y: * \

B *- - - - + - - - -* C

* : x *

* : *

* * *

The center of the sphere is

is the side view of the cone.

Note that:

The volume of a cone is: .**[1]**

In the diagram, we see that:

So we have: .**[2]**

The diagram also tells us that: .

Substitute into**[2]**: .

Can you finish up?

- Oct 31st 2006, 06:50 PMphilipsach1Thanks
Thank you so much! This really helped a lot.

It would be sooooo great if you could finish it up for me, I'm having so much trouble. Please and thank you. - Nov 1st 2006, 04:37 PMSoroban
Hello again, philipsach1!

The rest is "simple" Calculus . . . but okay.

We have: .

How do we maximize the volume?

We equate its derivative to zero and solve.

The function is: .

So: .

And we have the quadratic: .

. . which factors: .

. . and has roots: .

Since we want positive dimensions: .

. .

- Nov 1st 2006, 06:51 PMphilipsach1Thank you
Thanks so much! I really appreciate this.