Explanation

(b) The formula for rate of cooling is given by $= \frac{mc\theta}{t}$
As, mass = volume $\times$ density
Mass of sphere $= \frac{4}{3}\pi r^{3} \times \rho,$ where $\rho$ is density
Mass of unit area $= \frac{\frac{4}{3}\pi r^{3} \times \rho}{4\pi r^{2}} = \frac{1}{3}r\rho$
Hence, rate of cooling per unit area must be proportional to $r\ \rho$, (here $r$ is the radius of sphere and $\rho$ is the density
Hence, ratio of rate of cooling for two spheres is
$= \frac{r_{1}\rho_{1}}{r_{2}\rho_{2}}$
Where, $r_{1}:r_{2} = 1:2$ and $\rho_{1}:\rho_{2} = 2:1$
$= \frac{1}{2} \times \frac{2}{1} = 1:1$