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

I used to cut open a paper drinking cup in class when I was teaching this particular question.

It was easy to see that the resulting arc was equal to the circular base of the cup and the "slant" height of the cup was the radius of the partial circle.
Try this, and see if you can do the question.