Find the angle of the sector that should be removed from a circular piece of canvas so that the cone formed with the remaining canvas has the largest volume.
Have you derived the equation for the volume of the cone with some constant slantlength s (the radius of your circle), and some variable base b (the circumference of the remaining sector, a function of s and the removed angle t) ? Once derived, you can apply calculus to find its critical point(s) as function(s) of t.