Given, water is flowing at the rate of 0.7m/sec through a circular pipe whose internal diameter is 2cm

into a cylinder tank the radius of whose base is 40cm.

So, volume of the water coming out of pipe in half an hour  = Volume of the water in cylinder of base of radius 40 cm

Given, rate of flow of water = 0.7 m/sec  = 0.7*100 cm/sec = 70 cm/sec

So, the lenght of column traversed in half hour = 70*30*60 = 70*1800 cm

Now, volume of water flown out in half an hour = πr² h

                                                                           = π*1² * 70*1800

                                                                           = 70*1800π ............1

Let the level of the water will rise to a height of h cm

So, volume of the water in the cylindrical tank = π*(40)² h ............2

From equation 1 and 2, we get

      π*(40)² h = 70*1800π

=> 40*40*h = 70*1800

=> 16h = 70*18

=> h = (70*18)/16

=> h = (70*9)/8

=> h = (35*9)/4

=> h = 315/4

=> h = 78.75 cm

So, the increase in the level of water in half hour is 78.75 cm