Problem 1: Consider the sphere and the hollow cylinder below. The sphere can fit exactly into the cylinder. Consider the light blue surface area segments which are both of the same vertical height, h for the sphere S1 and the cylinder Sz and determine the difference in the two surface area segments Si and S2. Use multivariate calculus and show all your steps. 10 marks SI a R Problem 2: Use any irregularly shaped container (i.e. not strictly rectangular, spherical or cylindrical) around your home (examples shown in lecture) and determine its volume and surface area by the mathematical methods of curvilinear coordinates using multivariate calculus. Fill the container used with water to compare the accuracy of your calculated volume and measured volume. Include a photo of your container used. Show all your steps and justification for methods employed. 15 marks