MathematicsA rectangular water tank of base  11m×6m   contains water up to a height of 5m. If the water in the tank is transferred to a cylindrical tank of radius 3.5 m, find the height of the water level in the tank in cm.

A rectangular water tank of base  11m×6m   contains water up to a height of 5m. If the water in the tank is transferred to a cylindrical tank of radius 3.5 m, find the height of the water level in the tank in cm.


  1. A
    785
  2. B
    857
  3. C
    758
  4. D
    578 

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    Solution:

    We will first refer to the figures given below for better understanding.
    IMG_256 IMG_257Let us first calculate the volume of water in the rectangular tank.
    Length of rectangular tank = 11 m
    Breadth of rectangular tank = 6 m
    Height of rectangular tank = 5 m
    Volume of rectangular tank  V r =L×B×H  
    V r =11×6×5 V r =330 m 3 (1)  
    Radius of cylindrical tank = r = 3.5 m
    Height of cylindrical tank = h
    Volume of cylindrical tank  V c =π r 2 h  .
    V c = 22 7 × 3.5 2 ×h V c =38.5h(2)  
    As we know that the volume of water remains the same we can equate the equations (1) and (2).
    On equating we get,
    V c = V r  
    We get the height of the cylindrical tank as 8.57 m.
    38.5h=330 h= 330 38.5 h=8.57m  
    h=8.57×100 h=857cm  
    Hence, the height of water level in a cylindrical tank is 857 cm.
     
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