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A solid metallic cube having total surface area $\mathrm{24m^{2}}$ is uniformly heated. If it's temperature is increased by $\mathrm{10^{\circ}C}$ ,calculate the increase in volume of the cube. (Given $\mathrm{\alpha =5.0\times10^{-4} }^{^{\circ}}C^{-1}$ )
Option: 1
$\mathrm{2.4\times10^{6}cm^{3}}$

Option: 2
$\mathrm{1.2\times10^{5}cm^{3}}$

Option: 3
$\mathrm{6.0\times10^{4}cm^{3}}$

Option: 4
$\mathrm{4.8\times10^{5}cm^{3}}$

Answers (1)

best_answer

Area of Surface $\mathrm{=24m^{2}=6l^{2*}}\\$

Side length $\mathrm{\left ( l \right )}\\$ $\mathrm{=2m}\\$

Volume of cube $\mathrm{=8m^{3}}\\$

$\mathrm{\gamma = \alpha=15 \times 10^{-4}{ }^{\circ}C^{-1}}$

$\mathrm{\Delta T=10^{\circ} \mathrm{C}}$

For Volume expansion,

$\mathrm{\Delta V=V\gamma \Delta T}$

$\mathrm{=8\times 15\times 10^{-4}\times 10}$

$\mathrm{= 1200\times10^{-4}}$

$\mathrm{= 0.12m^{3}}$

$\mathrm{\Delta V= 1.2\times10 ^{5}cm^{3}}$

The correct answer is option 2.

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