The main idea here given the radius of the cone and the radius of the sphere, you can find height to start. Note this is similar to Example 9.1, which is covered in the recorded video lecture on the course page at ~23 minutes.

Once you find the height of the cone, you need to fit another sphere in the cone (which should be tangent to the base of the cone, the side of the cone, and the first sphere in the cone). A similar method can then be used to find the radius of this cone.

Hope this helps!