Explanation

(c) Energy radiated per unit time
$E = \sigma AT^{4}$
Where $\sigma = Stefan^{'}sconstant$
$\therefore$ For sun $E_{sun} = \sigma A_{sun}T_{sun}^{4}$
According to question
$E_{star} = 10000E_{sun}$
$\sigma A_{star} \times T_{star}^{4} = 10000 \times \sigma A_{sun} \times T_{sun}^{4}$
$\pi R_{star}^{2}T_{star}^{4} = 10000 \times \pi R_{sun}^{2} \times T_{sun}^{4}$
$\left( \frac{R_{star}}{R_{sun}} \right)^{2} = 10000\left( \frac{T_{sun}}{T_{star}} \right)^{4}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 10000\left( \frac{6000}{2000} \right)^{4}$
$\Rightarrow \ \ \ \ \ \ \frac{R_{star}}{R_{sun}} = \sqrt{10000 \times (3)^{4}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 100 \times 3^{2} = 900$
$R_{star}:R_{sun} = 900:1$