Question

Water flows at the rate of 10per minute through a cylindrical pipe having its diameter as 5mm. How much time will it take to fill a conical vessel whose diameter of the base is 40cm and depth 24cm?

Answer 1

Diameter of the pipe = 5 mm = 5/10cm = 1/2cm

∴ Radius of the pipe = 1/2 x 1/2cm = 1/4cm.

In 1minute, the length of the water column in the cylindrical pipe = 10m = 1000cm.

∴ Volume of water that flows out of the pipe in 1minute = π x 1/4 x 1/4 x 1000cm3.

Also, volume of the cone = 1/3 x π x 20 x 20 x 24cm3.

Hence, the time needed to fill up this conical vessel

= 256/5minutes = 51.2minutes.

Hence, the required time is 51.2minutes.