Answer
$R=4.1\times 10^9m$
Work Step by Step
As we know that
$P=e\sigma AT^4$
but surface area A is $A=4\pi R^2$
$\implies P=e\sigma 4\pi R^2T^4 $
This simplifies to:
$R=(\frac{P}{e\sigma 4\pi T^4})^\frac{1}{2}$
We plug in the known values to obtain:
$R=(\frac{3.4\times 10^{30}}{1\times 5.67\times 10^{-8}\times 4(3.1416) (23000)^4})^\frac{1}{2}$
$R=4.1\times 10^9m$
