MATH 215 Final: finalf13sol
Document Summary
Math 215 calculus iii, final exam, 12/17/2013: (10 points) let a be a number satisfying 0 < a < . (a) consider the ball b of radius r centered at the origin. The cone with opening angle a, given by the equation = a, divides the ball into two solids. Let ba be the solid containing the north pole (0, 0, r). (hence when a < /2, ba looks like an ice-cream cone with a spherical cap. ) Evaluate the ratio of the volume of ba to the volume of b. (recall that the volume of a ball of radius r is 4. Solution: vol(ba) = zzzba dv = z 2 . 2 (1 cos ). (b) consider the sphere s of radius r centered at the origin. The cone = a divides the sphere into two surfaces. Let sa be the surface containing (0, 0, r). Evaluate the ratio of the surface area of.
