A conical drinking cup is made from a circular piece of paper of radius R inches by cutting out a sector and joining the edges CA and CB. Find the radius, height and volume of the cone of greatest volume that can be made this way

Answer 1

The circumference of the original paper is

2πR

If the arc AB subtends an angle θ, then the circumference of the cone formed is

2πR - Rθ = R(2π-θ)

So, the radius of the cone is r = R(1-θ/2π)

Since the slant height of the cone is still r, the the altitude of the cone is

√(R^2 - r^2)