**Question:**

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 meters per second into a cylindrical tank. The water is collected in a cylindrical vessel radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?

**Solution:**

Given data is as follows:

Internal diameter of the pipe = 2 cm

Water flow rate through the pipe = 6 m/sec

Radius of the tank = 60 cm

Time = 30 minutes

The volume of water that flows for 1 sec through the pipe at the rate of 6 m/sec is nothing but the volume of the cylinder with n = 6

Also, given is the diameter which is 2 cm. Therefore,

R = 1 cm

Since the speed with which water flows through the pipe is in meters/second, let us convert the radius of the pipe from centimeters to meters. Therefore,

r = 1/100 m

Volume of water that flows for 1 sec = 22/7 × 1/100 × 1/100 × 6

Now, we have to find the volume of water that flows for 30 minutes.

Since, speed of water is in metres/second, let us convert 30 minutes into seconds. It will be 30 × 60

Volume of water that flows for 30 minutes = 22/7 × 1/100 × 1/100 × 6 × 30 × 60

Now, considering the tank, we have been given the radius of tank in centimeters. Let us first convert it into metres. Let radius of tank be ‘R’.

R = 60 cm

R = 60/100 m

Volume of water collected in the tank after 30 minutes = Volume of water that flows through the pipe for 30 minutes

22/7 × 60/100 × 60/100 × h = 22/7 × 1/100 × 1/100 × 6 × 30 × 60

h = 3 m

Therefore, the height of the tank is 3 metres.