# The surface temperature of Arcturus is about half as hot as the Sun’s, but Arcturus is about 100 times more luminous than the Sun. What is its radius, compared to the Sun’s?

##### 1 Answer

Arcturus's radius is 40 times larger than the sun's radius.

Let,

We are given,

Now express luminosity in terms of temperature.

The power radiated per unit surface area of a star is

To get the total power radiated by the star (its luminosity) multiply the power per unit surface area by the surface area of the star

Luminosity of a star

Using this,

where

Rearranging the above equation gives

We are given that

Arcturus's radius is 40 times larger than the sun's radius.