Question

Sphere maximum size curved on a wooden cylinder diameter 15 and height 12.What is volume of sphere

Answer 1

This problem is easy to solve when you convert the seemingly "3D" question into a representative 2D problem of maxium radius of the circle inside a triangle. The radius will be maximum when the triangle is equilateral triangle and the circle will be the incircle of the triangle.

As shown in the attached figure, OE=OD=radius of the incircle and triangle ABC is an equialteral triangle with OD ⊥⊥BC. Thus the triangle ODC is a 30-60-90 triangle and as BD=DC=6, ODCD=13√ODCD=13, giving you OD=23√