Question

two stars have the same luminosity. if star a has a hotter surface temperature than star b, then star b has a larger radius. star a has a larger radius. the two stars have the same radius.

Explanation:

The luminosity ($L$) of a star is given by the Stefan - Boltzmann law $L = 4\pi R^{2}\sigma T^{4}$, where $R$ is the radius, $\sigma$ is the Stefan - Boltzmann constant, and $T$ is the surface temperature. If $L_A = L_B$, then $4\pi R_{A}^{2}\sigma T_{A}^{4}=4\pi R_{B}^{2}\sigma T_{B}^{4}$, or $\frac{R_{A}^{2}}{R_{B}^{2}}=\frac{T_{B}^{4}}{T_{A}^{4}}$. Since $T_A>T_B$, then $R_A < R_B$.

Answer:

star B has a larger radius.