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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

= 53 c m 3

⇒ V = 125 c 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 × 1 c m 3 ⇒ V = 25 c m 3

Then, to determine the actual volume of the water-
Actual volume

= 125 c m 3 − 25 c m 3

⇒ Actual volume = 100 c m 3

Now, we will determine the volume of water when the cube is dropped-
Volume

= 125 c m 3 + 2 c m 3

⇒ V o l u m e = 127 c 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

⇒ V o l u m e = 27 c m 3

The side of cube-
Side

= 27 c m 3 3

⇒ S i d e = 3 cm

Hence, the volume of the cube is

27 c m 3

and the length of its edge is 3 cm.
Thus, option 4 is the correct option.

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