Question

Sides of a cube is made from $6$ identical sheets. If co-efficient of linear expansion of sheet is $\alpha$ and temperature is changed by $\Delta T$. Find the change in volume if side length of the cube is $a$.

• A. $a^3\alpha \Delta T$
• B. $2a^3\alpha \Delta T$
• C. $4a^3\alpha \Delta T$
• D. $3a^3\alpha \Delta T$

Answer 1

The correct option is D $3a^3\alpha \Delta T$

Side length of cube is $a$

$\therefore$ Volume $\left(V\right)$ of cube $=a^3$

During thermal expansion or contraction,

$\Delta V=V\gamma \Delta T$

$\Rightarrow \Delta V=\left(a^3\right)\times \left(3\alpha \right)\times \Delta T[\because \gamma =3\alpha ]$

$\Rightarrow \Delta V=3a^3\alpha \Delta T$

Hence, option $\left(d\right)$ is the correct answer.

$\begin{array}{c}\text{Why this question ?}\\ \text{Concept -Linear, Area and volume expansions are}\\ \text{related to each other. If}\alpha \text{is the linear expansion}\\ \text{co-efficient then,}\\ \text{Area expansion co-efficient,}\beta =2\alpha \\ \text{and Volume expansion co-efficient,}\gamma =3\alpha \end{array}$