Water flows out at the rate of 10 m/min from a cylindrical pipe of diameter 5 mm. Find the time taken to fill a conical tank whose diameter at the surface is 40 cm and depth 24 cm.

Using the volume formulas for a cone and a cylinder, the conical tank volume is (1/3) * pi * (20 cm)^2 * 24 cm = 3200 * pi cubic centimeters. The cylindrical pipe has a radius of 0.25 cm, so its cross-sectional area is pi * (0.25 cm)^2 = 0.0625 * pi square centimeters. Water flows at 10 meters per minute, which is 1000 centimeters per minute, giving a flow rate of 1000 * 0.0625 * pi = 62.5 * pi cubic centimeters per minute. The time to fill the tank is 3200 * pi / 62.5 * pi = 51.2 minutes. The time taken is 51.2 min.

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