Question

A star has a size of 0.1 solar radius. How many times larger is the sun than this star?

Answer 1

The sun's radius, diameter, and circumference are each 10 times the corresponding dimension of the junior star.

The sun's surface area is 100 times the area of the pygmy.

The sun's volume is 1,000 times the volume of the shrimp.

We can't determine anything about their density or mass.

Answer 2

In terms of radius, the Sun is simply 10 times larger.

In terms of volume, assuming that the star and the Sun are both perfect spheres (close enough), the volume can be calculated as such:
`V = (4)/(3) \pi r^3`.

Comparing the Sun and this star, the only thing in this formula that changes is the radius. The radius of the Sun is
`1 \ R_(sun)`, and the radius of the other star is
`0.1 \ R_(sun)`, but notice that the radius gets cubed.
`0.1^3 = 0.001`, and
`1^3 = 1`, so the Sun is
`10^3` times bigger, or three orders of magnitude, in terms of volume.