A solid metallic cube having total surface area 24 ~m^2 is...

A solid metallic cube having total surface area

24 \mathrm{~m}^2

is uniformly heated. If its temperature is increased by

10^{{}^{\circ}} \mathrm{C}

, calculate the increase in volume of the cube.

\left(\right.

Given :

\left.\alpha=5.0 \times 10^{-4}{ }^{{}^{\circ}} \mathrm{C}^{-1}\right)

Options

A $2.4 \times 10^6 \mathrm{ cm}^3$
B $1.2 \times 10^5 \mathrm{ cm}^3$
C $6.0 \times 10^4 \mathrm{ cm}^3$
D $4.8 \times 10^5 \mathrm{ cm}^3$

Correct answer

B. $1.2 \times 10^5 \mathrm{ cm}^3$

Step-by-step solution

We have

\Delta V=V_0 \gamma \Delta T\Delta V=a^3,(3 \alpha) \Delta T

Now,

6 a^2=24 \quad[\because

Total surface area of cube \left.=6 a^2\right]\Rightarrow a^2=4 \Rightarrow a=2

So,

\Delta V=2^3\left(3 \times 5 \times 10^{-4}\right) \times 10=1200 \times 10^{-4} \mathrm{~m}^3=1200 \times 10^2 \mathrm{~cm}^3=1.2 \times 10^5 \mathrm{~cm}^3

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