Let AH} he the area of a circle 1with radius t], at time t in min. Suppose the radius is changing d1" at the rate of E = i3 tttmin. Find the rate of change at the area at the moment in time when r = El. dA _ E _ E ftgfmiu. A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 5 ft/s. How rapidly is the area enclosed by the ripple increasing when the radius is 3 feet? Answer: E ft2 /sA spherical snowball is melting in such a way that its diameter is decreasing at rate of 3 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 6 cm? Answer: E cm3 / min.You are blowing air into a spherical balloon at a rate of 11 cubic inches per second. Given that the radius of the balloon is 3 inches when t = 3 seconds answer the following questions: (a) How fast is the radius of the balloon growing at t = 3 seconds Answer: E inches per second. (b) What is the rate of change of the surface area at t = 3 seconds? Answer: E square inches per second.The height of a triangle is increasing at a rate of 2 cm/min while the area of the triangle is increasing at a rate of 8 square cm/min. At what rate is the base of the triangle changing when the height is 1 centimeters and the area is 3 square centimeters? Answer: cm/min.The top of a 10 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 5 feet per second. How fast is the bottom of the ladder sliding along the ground away from the wall when the bottom of the ladder is 6 feet away from the base of the wall? Answer: ft/s.A boat is pulled into a dock by a rope attached to the bow (front end) of the boat and passing through a pulley on the dock that is 12 m higher than the bow of the boat. If the rope is pulled in at a rate of 2 m/s, at what speed is the boat approaching the dock when it is 5 m from the dock? Answer. m/s.A street light is at the top of a pole that is 13 feet tall. A woman 6 it tall walks away from the pole with a speed of 5 ft/sec along a straight path. How fast is the length of her shadow moving when she is 10 ft from the base of the pole? Answer: ft/sec.Gravel is being dumped from a conveyor belt at a rate of 7 cubic feet per minute. It forms a pile in the shape of a right circular cone whose height and base diameter are always equal to each other. How fast is the height of the pile increasing when the pile is 4 feet high? Answer: 3 ft/min.A filter filled with liquid is in the shape of a vertex-down cone with a height of 9 inches and a diameter of 6 inches at its open (upper) end. If the liquid drips out the bottom of the filter at the constant rate of 1 cubic inches per second, how fast is the level of the liquid dropping when the liquid is 2 inches deep? Answer: E in/sec.At noon, person A is 3 miles east of person B. Person A is walking east at 5 miles per hour and person B is walking north at 6 miles per hour. Noon 6 nph 3 ni 5 mph B A (You can click on the graphic to enlarge the image.) How fast is the distance between the people changing at 2 PM? Answer: miles / hr.A trough is Z = 10 it long and has a cross section of an isosceles trapezoid with base of b = 3 ft, height of h = 1 ft, and top of t = 6 it (see picture below). h b (You can click on the graph to enlarge the image.) If the trough is being filled with water at a rate of 10 fto/min how fast is the water level rising when the water is 2 inches deep? Answer. E ft/min