Question

A $700\text{g}$ solid cube having an edge of length $10\text{cm}$ floats in water. How much volume of the cube is outside the water? Density of water $=1{\text{g/cm}}^3.$

• A. $700{\text{cm}}^3$
• B. $300{\text{cm}}^3$
• C. $1000{\text{cm}}^3$
• D. $30{\text{cm}}^3$

Answer 1

The correct option is B $300{\text{cm}}^3$

The weight of the cube is balanced by the buoyant force. The buoyant force is equal to the weight of the water displaced. If $V$ volume of the cube is inside the water, the weight of the displaced water $=V\rho g,$ where $\rho$ is the density of water. Thus,
$V\rho g=mg$

$\Rightarrow V\rho g=700\times g$
$\Rightarrow V=\frac{700}{\rho }=700{\text{cm}}^3$
The total volume of the cube $=(10\text{cm}{)}^3=1000{\text{cm}}^3.$
$\therefore$ The volume of cube outside the water is $1000{\text{cm}}^3-700{\text{cm}}^3=300{\text{cm}}^3$