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The temperature of a metallic sphere of radius R is increased by a small amount $\Delta T$. If the linear coefficient of thermal expansion of the metal is $\alpha$, the approximate increase in the volume of the sphere is:
Detailed Solution
$\gamma=\frac{\Delta V}{V}\times\frac{1}{\Delta T}$ with $\gamma=3\alpha$. $\Delta V=3\alpha\Delta T\times V=\frac{4}{3}\pi R^3\times3\alpha\Delta T=4\pi R^3\alpha\Delta T$.