3. The base of a solid is a circle of radius a meters and cross sections perpendicular to its base are squares. a. Find the volume of the solid as a function of a. Spots b. Find the value of a if the volume of the solid is 10m' Spots 4. A spherical water tank with an inner radius of 8 m has its lowest point s in above the ground. It is filled by a pipe that feeds the tank at its lower poilit (see figure). Assuming that the water source is at ground level, inflow pipe 2 m a. Neglecting the volume of the inflow pipe, how much work is needed to fill the tank if it is initially empty? Express your answer in terms of it and g (the constant acceleration due to gravity). Spto b. If the lowest point of the tank is now at the ground level and the inflow pipe, still vertical and 2 m long, feeds the tank at its highest point, neglecting the volume of the inflow pipe, how much work in terms of T and g would be required to fill the tank if it is initially empty?5. Evaluate dx xIn .x 6. Integrate by parts [ x(In x) dx. Make sure you show your work. 7. Integrate [ sin' 3x dx. Make sure you show your work. 8. Find the definite integral (1+3)/Make sure you show your work