# Re: cone inside sphere problem - find the dimensions of the cone of max volume

*From*: rob@xxxxxxxxxxxxxx (Rob Johnson)*Date*: Wed, 30 Nov 2005 07:31:44 GMT

In article <26801510.1133296839363.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxx>,

jdavca <msfca@xxxxxxxx> wrote:

>Problem:

>The vertex of a right circular cone and the circular edge of its base

>lie on the surface of a sphere. The sphere has a radius of 5 feet.

>Find the dimensions of the cone of maximum volume that can be fitted

>into the sphere.

>

>I'm really not sure what to do with this one!

>

>I appreciate anyone who can help me with this...

Let h be the height of the cone and r be the radius of the base of the

cone. Note that the distance from the center of the sphere to the base

of the cone is |h-5|. From the point on the base of the cone closest

to the center to the edge of cone is r. Use Pythagoras to find the

distance from the center of the sphere to the edge of the cone. Note

that this distance is also 5. This should give you a relation between

r and h.

To maximize volume, you want to maximize hr^2.

Rob Johnson <rob@xxxxxxxxxxxxxx>

take out the trash before replying

.

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