Explanation

(d) From Stefan law, the energy radiated by sun is given by. $P = \sigma eAT^{4}$, assuming e=1 for sun.
In Ist case, $P_{1} = \sigma e \times 4\pi R^{2} \times T^{4}$
In 2nd case, $P_{2} = \sigma e \times 4\pi\left( 2R^{2} \right) \times (2T^{4})$
$= \ \sigma e \times 4\pi R^{2} \times T^{4} \times 64 = 64P_{1}$
The rate at which energy is received by earth is,
$E = \frac{P}{4\pi R_{SE}^{2}} \times A_{E}$
where $A_{E}$= area of earth
$R_{SE}$= distance between sun and earth
So, In Ist case, $E_{1} =$ $\frac{P_{1}}{4\pi R_{SE}^{2}} \times A_{E}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ E_{2} = \frac{P_{2}}{4\pi R_{SE}^{2}} \times A_{E} = 64E_{1}$