Q. 215.0( 4 Votes )

Water is flowing

Answer :




Let the length of pipe filling the tank be x m.


Given the diameter of the pipe is 14cm


radius = 7cm


= 0.07m


Now the pipe is in shape of the cylinder, so the volume of the pipe, VP becomes,


VP = πr2h


Substituting the corresponding values, we get


VP = π(0.07)2(x)


VP = (0.0049) πx m3………..(i)


Now the water tank is rectangular, so it will be in the form of the cuboid.


So, given the length of the tank, l = 50 m long


and given the breadth of the tank, b = 44 m wide


We need to find the level of water in the tank will rise by 21cm, hence this will be the height, i.e., h = 21cm = 0.21m


So, the volume of the tank, VT, will be


VT = lbh


Substituting the corresponding values, we get


VT = 50 × 44 × (0.21)


VT = 462m3…………. (ii)


Now as the pipe is filling the water, so


The volume of the pipe should be equal to the volume of the tank, i.e.,


VP = VT


Substituting values from equation(i) and (ii), we get


(0.0049) πx = 462






x = 30000m


= 30km


This is the length of the pipe.


And it is given water in the pipe is flowing at the rate of 15km/hr, means


15km travels in the pipe in = 1hour


1km travels in the pipe in


So, in 30km long pipe water travels in


= 2 hr


So, in 2 hours the level of water in the tank will rise by 21cm.


OR


As the solid sphere is melted and recast into three small spherical balls, so


The volume of the big sphere = volume of small balls


 The volume of big sphere = number of small balls × volume of small balls ……(i)


We know, the volume of the sphere


And let the radius big sphere, R = 3cm


And given diameter of small sphere = 0.6cm, so the radius of each small sphere,



= 0.3 cm


And let the number of balls be n


Substituting this in equation (i), we get



Canceling the like terms, we get


R3 = n × r3


Substituting corresponding values, we get


(3)3 = n × (0.3)3


27 = n × (0.027)





n = 1000


Hence 1000 number of balls can be made from the big sphere.

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