I need help with an optimization problem!

[Highschooler]

So imagine that there is a sphere with a radius of 1 in. I am trying to find the dimensions of the cone with the smallest surface area that the sphere fits inside of without breaking the top plane of the cone.
I know that the volume of the sphere is 4pi/3, and the equation for surface area of a cone is S=pi*radius at the base*Length of the outside edge. HELP D:

 

[Deleted member 4993]

So imagine that there is a sphere with a radius of 1 in. I am trying to find the dimensions of the cone with the smallest surface area that the sphere fits inside of without breaking the top plane of the cone.
I know that the volume of the sphere is 4pi/3 , and the equation for surface area of a cone is S=pi*radius at the base*Length of the outside edge. HELP D:

Do a similar but different problem first:

Find the radius of the largest circle that can fit inside a given (isosceles) triangle.

That will give you pretty good idea about the path you need to take to solve the problem.

Tell us what do you find....