Step 1: Underlying Concept:
The three coefficients of thermal expansion are related: \(\gamma = 3\alpha = 3\beta/2\), where \(\alpha\), \(\beta\), \(\gamma\) are linear, area, and volume expansion coefficients.
Step 2: Explanation:
Percentage change in radius \(= \alpha\Delta\theta\). Percentage change in volume \(= \gamma\Delta\theta = 3\alpha\Delta\theta\). Percentage change in density \(= -\gamma\Delta\theta/(1+\gamma\Delta\theta) \approx -3\alpha\Delta\theta\) in magnitude. Volume change is \(3\times\) radius change, and is numerically the largest positive change.
Step 3: Conclusion:
Percentage change is maximum in volume.