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 ____.

Question

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 ____.

Accepted Answer

Volume of a cube is

l
    3

,Volume of a cuboid is

l×b×h
   , 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 levelThe 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 thatThe 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+300x−300h=3375

⇒300x=3375

⇒x=
      
       3375
      
       300

∴x=11.25cm

The rise in water level 11.25 cm.

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 $20 c m × 15 c m$ .The rise of water level is ____.

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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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Detailed Solution

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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 $20 c m × 15 c m$ .The rise of water level is ____.