Use the radius-luminosity-temperature relation to calculate the radius of a red supergiant with temperature 3000 K and total luminosity 10000 times that of the Sun.

The radius of the red supergiant is .

Explanation:

The radiant power establishes how much energy an observer or a detector can get from a luminous source per unit time and per unit surface area.

 (1)

Where is the radiant power received from the source, L its intrinsic luminosity and r is the distance.

The Stefan-Boltzmann law is defined as:

 (2)

Where is the radiant power, is the Stefan-Boltzmann constant and T the temperature.

Then, equation 2 can be replaced in equation 1

(3)

Notice that L is the energy emitted per second by the source.

Therefore, r can be isolated from equation 3.

 (4)

The luminosity of the Sun can be estimated isolating L from equation 3.

but, and for the Sun.  

The following expression can be used to find the luminosity of the star:

Finally, equation 4 can be used.

Hence, the radius of the red supergiant is .

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