Question:
The radius of a metal sphere at room temperature T is R, and the coefficient of linear expansion of the metal is α. The sphere is heated a little by a temperature ∆T so that its new Temperature is T + ∆T. The increase in the volume of the sphere is approximately
(a) $2 \pi R \alpha \Delta T$
(b) $\pi R^{2} \alpha \Delta T$
(c) $4 \pi R^{3} \alpha \Delta T / 3$
(d) $4 \pi R^{3} \alpha \Delta T$
Solution:
The correct answer is (d) $4 \pi R^{3} \alpha \Delta T$