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Q.

A horizontal table supports a rectangular container that holds water up to 1 cm from the top and has a square base with a side measurement of 5 cm. When a cube is submerged in water, 2 cubic centimeters of water overflow and the water rises to the top of the cube.


What is the length of its edge?


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a

8 cm

b

6 cm

c

1 cm

d

3 cm 

answer is D.

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Detailed Solution

Given that, a rectangular container that holds water up to 1 cm from the top and has a square base with a side measurement of 5 cm.
We have to find the length of the edge.
Formula that we will require to solve this question
The volume of a cube l 3   where l is the edge of the cube.
 First, we will find the volume of the container with square base-
Volume = 5 3 c m 3  
⇒V=125c m 3  
Considering that the left portion is 1 cm less occupied than the top, we must now determine its volume
Formula that we will require to solve this question
Volume of a cuboid =l×b×h   where l, b, h are length , breadth and height of the cuboid.
  V=5×5×1c m 3 ⇒V=25c m 3  
Then, to determine the actual volume of the water-
Actual volume =125c m 3 −25c m 3  
⇒Actual volume=100c m 3  
Now, we will determine the volume of water when the cube is dropped-
Volume =125c m 3 +2c m 3  
⇒Volume=127c m 3  
And, the volume of cube dropped-
Volume of cube = Volume of water after cube is dropped - volume of water before
Volume =127-100
⇒Volume=27c m 3  
The side of cube-
 Side = 27c m 3 3  
⇒Side=3cm  
Hence, the volume of the cube is 27c m 3   and the length of its edge is 3 cm.
Thus, option 4 is the correct option.
 
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