MathematicsA cube of edge 15 cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of the vessel are  20cm×15cm  .The rise of water level is ____.

A cube of edge 15 cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of the vessel are  20cm×15cm  .The rise of water level is ____.


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    Solution:

    Volume of a cube is  l 3  ,
    Volume of a cuboid is  l×b×h   ,
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    We are given that a cube of edge 15 cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base of the vessel are 20cm×15cm  .
    To find: rise in water level
    The volume of rectangular vessel before immersing is l×b×h  .
    l=20cm,b=15cm,h=hcm Volum e before =20×15×h=300hc m 3  
    The volume of rectangular vessel after immersing is l×b×h  .
    l=20cm,b=15cm,h= h+x cm Volum e after =20×15× h+x =300 h+x c m 3  
    Volume of the cube is l 3  .
    l=15cm Volum e cube = 15 3 =15×15×15=3375c m 3  
    Statement 1: The increase in volume of water is the volume of the rectangular container after immersion minus the volume of the rectangular container before immersion.
    Statement 2: The increase in volume of water is equal to the volume of the submerged cube.
    From the above statements, we assume that
    The volume of the submerged cube is equal to the volume of the rectangular container after immersion minus the volume of the rectangular container before immersion.
    Volum e cube =Volum e after Volum e before Volumeafter=300(h+x)c m 3 ,Volum e before =300hc m 3  
    Volum e cube =3375c m 3 3375=300(h+x)300h 300h+300x300h=3375 300x=3375 x= 3375 300 x=11.25cm  
    The rise in water level 11.25 cm.
     
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