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Q.

A cube of 9 cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base are 15 cm and 12 cm, then what is the rise in water level in the vessel?


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a

4.05 cm

b

4.10 cm

c

4.80 cm

d

4.20 cm 

answer is A.

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Detailed Solution

Given-
 A cube of 9 cm edge is immersed completely in a rectangular vessel containing water.
The dimensions of the base are 15 cm and 12 cm.
To find- the rise in water level in the vessel.
We will first determine the volume of the cube.
The volume of a cube = l 3   where l is the length of the cube.
Volume =9×9×9c m 3 =729c m 3  
Now, we will determine the volume of the cuboid.
The volume of a cuboid =l×b×h  , where l is the length, b is the breadth and h is the height of the cuboid.
Volume =15×12×hc m 3  
⇒Volume=180h  cm 3  
The volume of the cube will be equal to the volume of water displaced in the cuboid.
To find the rise in water level in the vessel-
⇒729=180×h
⇒h=729180
⇒h=4.05cm
Thus, the rise in water level in the vessel is 4.05 cm.
Hence, option 1 is the correct option.
 
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