DEFINITION 1. Given a subset S C R2 we define the cone induced by S of height h as the set C C R3 consisting of points in any line segment connecting (0, 0, 0) and a point in the set {(x, y, z) ER' : (y, z) ES, x = h}. Exercise 2. Let E C R2 be the region of R2 contained inside an ellipse whose major radius is 3 and minor radius is 2. a) Determine the area of E. Hint: Assuming that E is centred at the origin, show that the perimeter of E can be expressed by the equation () + ()= 1. Use this to find an integral that allows you to find the area of E. Use a change of variables to relate the area of the ellipse to the area of a circle. Does the area of the ellipse depend on its position? b) Use the previous point to find the volume of the cone induced by E of height 5. Hint: Find first the volume of a cone where the base is centred at the origin. Provide an argument to show that the volume of the cone does not depend on where the centre of the base is located