# Max and min

#### leprofece

##### Member
(1) Confine to a hemisphere of RADIUS r a volume minimum Cone; the plane of the base of the cone matches with the basis of the hemisphere. Find the height of the cone.

Answer is H = (sqrt of 3) R

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#### MarkFL

Staff member
I think if the two objects have their bases in the same plane, the the height of the cone must be the same as the radius of the hemisphere, so I think more likely the case is that the vertex of the cone on on the base of the hemisphere. Even so I get a result that is very similar to, but critically different than what you have given.

1.) What is your objective function?

2.) Can you express the radius of the cone in terms of the radius of the hemisphere and the height of the cone? Look at a cross-section through the center of both objects and Pythagoras will be your friend.

What do you find?

#### leprofece

##### Member
Ok it is a problem of derivative applications Maximum and minimum we must get two functions and derive one to get the minimum.
In this problem I dont have idea of the functions maybe the volume of the cone and thales
as i said before they are very difficult problems.