* Radius and Volume: The volume of a sphere (like a star) is calculated using the formula (4/3)πr³, where 'r' is the radius.

* Comparing Volumes: To find how much larger the Sun is, we'll compare the volumes of the Sun and the smaller star.

Calculations:

1. Sun's Volume: Let's assume the Sun has a radius of 1 (for simplicity). Its volume would be (4/3)π(1)³ = (4/3)π.

2. Smaller Star's Volume: The smaller star has a radius of 0.1, so its volume is (4/3)π(0.1)³ = (4/3)π(0.001).

3. Ratio: To find how much larger the Sun is, divide the Sun's volume by the smaller star's volume:

[(4/3)π] / [(4/3)π(0.001)] = 1 / 0.001 = 1000

Answer: The Sun is 1000 times larger than a star with a radius of 0.1 solar radii.