According to the Stefan-Boltzmann law, the power ($P$) radiated by a spherical black body is given by $P = \sigma A T^4 = \sigma (4\pi r^2) T^4$, where $r$ is the radius and $T$ is the absolute temperature. Let the initial power be $P_1 = 450\text{ W}$ with radius $r_1 = 12\text{ cm}$ and temperature $T_1 = 500\text{ K}$. When the radius is halved ($r_2 = r_1 / 2$) and the temperature is doubled ($T_2 = 2T_1$), the new power $P_2$ will be: $P_2 = \sigma 4\pi (r_1 / 2)^2 (2T_1)^4$ $P_2 = \sigma 4\pi \left(\frac{r_1^2}{4}\right) (16T_1^4)$ $P_2 = 4 \times [\sigma (4\pi r_1^2) T_1^4]$ $P_2 = 4 \times P_1$ $P_2 = 4 \times 450\text{ W} = 1800\text{ W}$. Therefore, the power radiated would be $1800\text{ W}$.