A paper drinking cup lled with water has the shape of a cone with height h and semi-vertical angle
(refer to the gure). A ball is placed carefully in the cup thereby displacing some of the water and making
it over
ow. What is the radius of the ball that causes the greatest volume of water to spill out of the cup?

Question

A paper drinking cup lled with water has the shape of a cone with height h and semi-vertical angle 
(refer to the gure). A ball is placed carefully in the cup thereby displacing some of the water and making
it over
ow. What is the radius of the ball that causes the greatest volume of water to spill out of the cup?

anonymous · Answer

r/h= [sin(a)] / [sin(a) + cos(2a)]