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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 × 9 c m 3 = 729 c 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 × h c m 3

⇒ V o l u m e = 180 h 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-

\Rightarrow 729 = 180 \times h

\Rightarrow h = \frac{729}{180}

\Rightarrow h = 4.05 cm

Thus, the rise in water level in the vessel is 4.05 cm.
Hence, option 1 is the correct option.

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