A square glass tank with side length 10m is half filled with water. (15 marks) A solid metal cylinder of radius 2m and height 12m is being pushed vertically into the centre of the tank water as in the picture below. W At any time, the speed at which the cylinder is being lowered into the the tank (measured in meters per minute) is the same as the distance between the base of the cylinder and the bottom of the tank (measured in meters). Water Level: The water level is the height of the water from the bottom of the cube. Hint: The volume V of a cylinder with any base is given by V = At . h, where A, is the area of the base and h the height of the cylinder. (a) (3 marks) What is the volume of water V. in the tank? What is the volume V of water in the "b section" of the tank (below the bottom of the cylinder)? VO =What is the volume of water V, in the "h section" of the tank (above the bottom of the Compare the volumes calculated in (a) and (b) to find an equation that relates b and w. Equation relating b and w: How quickly is the water level on the side of the tank rising when the base of the cylinder he bottom of the tank? Water Level is rising at the rate of metres/minute