Question

water flows at the rate of 10 meter per minute through a cylindrical pipe having its diameter at 5 mm. how much time will take to fill a conical vessel where diameter of base is 40 cm and depth 24 cm?

Answer 1

Radius of the pipe = 5/2 mm = 5/2 x 1/10 cm = 1/4 cm

Speed of water = 10 m/min = 1000 cm/min

Volume of water that flows in 1 minute = Π r2 h = 22/7 x 1/4 x 1/4 x 1000 = 1375/7 cm3

Radius of conical vessel = 40/2 = 20 cm; Depth = 24 cm

Therefore, Capacity of the vessel = 1/3 x Π r2 h

= 1/3 x 22/7 x 20 x 20 x 24 = 70400/7 cm3

Therefore, Time required to fill the vessel = capacity of the vessel / volume of water flowing per minute

= 70400/7 / 1375/7 = 70400/7 x 7/1375 = 256/5 minutes = 51 min 12 sec