Find temperature of surface (Blackbody Radiation) 
An astronomer is trying to estimate the surface temperature of a star with a radius of $5 \times 10^8\ m$ by modeling it as an ideal blackbody. The astronomer has measured the intensity of radiation due to the star at a distance of $2.5 \times 10^{13}\ m$ and found it to be equal to $0.055\ W/m^2$. Given this information, what is the temperature of the surface of the star?

How do I do this? The hint was to use $I=\sigma T^4$ (where $\sigma = 5.67 \times 10^{-8}$).
Others: 

As the star radiates energy, the total power that flows through any
  spherical surface concentric with the star remains constant. The total
  power flowing through such a surface can be obtained by multiplying
  the intensity (power per square meter) by the surface area of the
  sphere. 
Using the law of conservation of energy, the surface area of
  the two spheres (one at the star's surface and one with the radius
  equal to the observing distance), and the intensity measured by the
  observer at the observing distance, you should be able to obtain the
  intensity at the surface of the star.

Don't really understand the 2nd paragraph too ... 
 A: The idea is just to make use of the relationship between luminosity (the amount of energy emitted per second from the star - in other words, the power) and flux (the amount of power hitting the surface).
Because, the flux can be modeled as a large number of (imaginary) spherical energetic wavefronts emerging from the star in 3-D space as a function of time. Also, this flux is based on the inverse-square law. So, it decreases with distance (squared). And since the power distributed over every sphere is still the same, both are related by the area of spheres.
$$\mathrm{Flux=\frac{Luminosity}{4\pi r^2}}$$
And since the question says that the astronomer idealizes it as a blackbody (which we always do), we can use the Stefan-Boltzmann equation and say that the flux is $\sigma T^4$...

Edit for confusion: Simply relating the given flux with Stefan-Boltzmann only gives the temperature of the imaginary sphere at the distance at which the flux was measured. First, you can find the luminosity of the star by using the relation above. Then, you need the flux at the surface of the star. Given the radius of star, it can be used to determine how much power is transmitted to the surface through the luminosity. Finally on relating with $\sigma T^4$ gives the answer...
