Math Xb Spring 2004 NameLab 2: Related Rates Section InstructorFebruary 19, 2004 Collaborators1. Two concentric circles are expanding, the outer radius at a rate of 2 feet per second and the inner oneat a radius of 5 feet per second. At a certain instant, the outer radius is 10 feet, and the inner radius is3 feet. At this instant, is the area of the ring between the two circles increasing or decreasing? Justifyyour answer.2. A baseball diamond is a square with side 90 feet. The corners of the square are labeled home plate,first base, second base, and third base as one moves around the square counter-clockwise. A batterhits the ball and runs from home plate towards first base with a speed of 24 fee t pe r sec ond.(a) At what rate is his distance from second base changing when he is halfway to first base?(b) At what rate is his distance from third base changing at the same moment?3. Water is leaking out of an inverted conical tank at a rate of 10,000 cubic centimeters per minute atthe same time that water is being pumped into the tank at a constant rate. The tank has height 6meters and the diameter at the top is 4 meters. If the water level is rising at a rate of 20 centimetersper minute when the height of the water is 2 meters, find the rate at which water is being pumped intothe