The radius of a metal sphere at room temperature T is R and the coefficient of linear expansion of the metal is $\alpha$. The sphere 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:

1. $2\mathrm{\pi R\alpha }∆\mathrm{T}$

2. ${\mathrm{\pi R}}^2\mathrm{\alpha }∆\mathrm{T}$

3. $4{\mathrm{\pi R}}^3\mathrm{\alpha }∆\mathrm{T}/3$

4. $4{\mathrm{\pi R}}^3\mathrm{\alpha }∆\mathrm{T}$