I am solving this problem using a software called maple, but if you do not have that an answer solved out using integrals would also work. 3) An art student was given a circular metal disk 2 feet in diameter and told to drill a small hole in it so that when the disk was cut in half and the piece with the hole was placed atop a spike stuck in the hole, it would balance. Not knowing about integration, the artist drilled a hole at a point halfway between the center and the edge. a) Where should the art student have drilled the hole? (Hint: Consider the right half of the circle \( x^{2}+y^{2}=1\).) b) Now that he has made the mistake, he decides that rather than drill a second hole, he will cut the piece with the hole in it in such a way that it will balance on the spike at the point of the hole. Where should he cut the piece? c) What is the area of the piece of the metal disk that balances at the point where the hole was drilled?