MathematicsIf a marble of radius 2.1cm is put into a cylindrical cup full of water of radius 5cm and height 6cm then how much water flows out of the cylindrical cup?

If a marble of radius 2.1cm is put into a cylindrical cup full of water of radius 5cm and height 6cm then how much water flows out of the cylindrical cup?


  1. A
    55.4  cm 3  
  2. B
    38.8  cm 3  
  3. C
    19.4  cm 3  
  4. D
    471.4  cm 3   

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    Solution:

    Given,
    The radius of marble is 2.1 cm
    The radius of cylindrical cup is 5 cm
    The height cylindrical cup is 6cm.
    We know as per Archimedes principle,
    Volume of water flows out of cylindrical cup = Volume of marble
    Volume of marble is given by 4 3 π r 3  .
    Volume if water that flows out of the cylindrical cup = volume of marble
    We get,
    Volume of water flows out of the cylindrical cup= 4 3 π r 3 4 3 × 22 7 × (2.1) 3 38.81c m 3   Therefore, the amount of water flows out of the cylindrical cup is 38.8 cm 3  .
    Hence, the correct option is 2.
     
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