Note: Give exact answers where possible (for example, is exact but 3.142 is approximate).

5. Hi? marks] Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves 1! = x2 and I = 3;: about the line I = 1. 6. [It] marks] The base of a solid is the region bounded by the parabolas y = x2 and y = 2 :2. Find the volume of the solid if the cross sections perpendicular to the .r-axis are equilateral triangles. T. [It] marks] Find the volume of the solid 3 if the base of 3 is the triangular region with vertices {13,11}, {3,11}, and {13,2} and cross sections perpendicular to Iiiaxis are semi circles. 8. [3 marks] A log If} m long is cut at 1-metre intervals and its crosssectional areas {at a distance I from the end of the log] are given in the table. Use the Midpoint Rule with n = 5 to estimate the 1volume of the log. "HUI-mu IIII-I-IIIM 9. {12 marks] A conical tank rests on a platform that is It] metres above a large lake. The circular base of the tank has a radius of 4 metres and the top of the tank is 15 metres above the surface of the lake. How much work must be done to fill the tank with water from the lake it it is to be pumped in through an outlet at the bottom of the tank? Set up your coordinate system so that I = [1 corresponds to the top of the tank and I = 5 corresponds to the base of the tank, which rests on the platform. Use the fact that the density of water is 111m kgfm3 and g = 9.3 mjsz