c.

i.As a star runs out of hydrogen to fuel nuclear fusion in its core, changes within the star usually cause it to leave the main sequence, expanding and cooling as it does so. Would a star with a radius 12 times that of the Sun, but a surface temperature 0.3 times that of the Sun, be more, or less luminous than the Sun?

Show and explain your reasoning.

You may assume the surface area of a sphere is A = 4r².

(Hint: you will need to consider the proportional effect on stellar luminosity of both the change in the surface area and the change in surface temperature of a star, as implied by Equation 4.2 (see Topic 10: Section 4.1.2). It isn't necessary to input actual values.)