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



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>
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