Discussion
When a metallic sphere is heated, maximum percentage change will be observed in its
Answer: A
The largest percentage change is in its volume.
If the linear expansion coefficient is \(\alpha\), a small temperature rise \(\Delta T\) changes every length (radius, diameter) by a fraction \(\alpha\Delta T\). Area depends on length squared and volume on length cubed, so for small changes:
\[ \begin{aligned} \frac{\Delta r}{r} &= \alpha\Delta T, \quad \frac{\Delta A}{A} = 2\alpha\Delta T \\ \frac{\Delta V}{V} &= 3\alpha\Delta T \end{aligned} \]
Volume changes by three times the percentage of the radius, more than any other option. Radius and diameter change by the same percentage, the smallest. Mass does not change at all on heating.
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