Question

A solid cube of side length $k$ is dropped into a cubical vessel partly filled with water. The length of side of the vessel is 200% more than the length of the solid cube. If the solid cube is completely submerged, then the increase in water level in the vessel is

• A. $\frac{k}{27}$
  
• B. $\frac{k}{9}$
  
• C. $\frac{k}{3}$
  
• D. 3$k$

Answer 1

The correct option is B $\frac{k}{9}$


Given that the side of a solid cube is $k$.
∴ Volume of the solid cube $=k^3$
Length of cubical vessel $=k+200\%$ of $k$
= $k+2k$
= $3k$
Let the increase in water level in the vessel be $h$.
According to the question:
Volume of solid cube = Volume of water increased in the vessel
$\Rightarrow k^3=3k\times 3k\times h$
$\Rightarrow k^3=9k^{2}h$
$\Rightarrow h=\frac{k}{9}$
Therefore, the increase in the water level in the vessel is $\frac{k}{9}$.
Hence, the correct answer is option (b).