Explanation

(b) Stefan’s law states that the rate of emission of radiant energy by unit area of perfectly black body is directly proportional to the fourth power of its absolute temperature.
$E \propto AT^{4}\ \ $
$\ \ \ or\ \ \ \ E \propto r^{2}$
($\because\ \ A = \pi r^{2}\ and\ T$ is same for both the spheres where $r$ is radius of sphere.)
$\frac{E_{1}}{E_{2}} = \frac{r_{1}^{2}}{r_{2}^{2}} = \left( \frac{2}{1} \right)^{2} = \frac{4}{1} = 4:1$