Q12. A tank is shaped like a prism whose faces are semicircles of radius 3m, as in the figure to the right. The prism is 5m x (meters) long, and it is filled with water. The goal of this question is to determine the total work required to pump all of its water to a height of 2m above the top of 3 - the tank. Recall: the density of water is p = 1000 kg/m3 and the acceleration due 5m to gravity on Earth's surface is g = 9.8 0- m/s2. (a) [2 points] Let x be the height (in m) measured from the bottom of the tank. Find an expression for the approximate volume V(x) of a thin layer of water between heights x m and a + Ax m. Justify your answer. (Note: doing a drawing may be helpful.) (b) [2 points] Give a definite integral that computes the total work required to pump all of the water in the tank to a height of 2m above its top. (Do not evaluate the integral.)