Lesser the radius the lesser the volume. Why?

[avito009]

If we take two planets One Earth and another one with half the radius of Earth. The planet with half the radius has lesser than half of the volume of the Earth. Also given that mass is half. Why?

Is it because lower radius and lesser mass means lesser gravity and lesser gravity can pull lesser matter towards the core?

 

[ShayanJ]

Radius and volume of a sphere are related by $V=\frac{4}{3} \pi R^3$. Its completely geometrical and has nothing to do with physics!

 

[Carno Raar]

http://imgur.com/UKHLp4n

Doubling all dimensions means 8x the volume and mass. Halving all the dimensions means 1/8 the volume and mass.

Looking at these cubes in the image link should explain it very intuitively. If there are 2 cubes per side there are a total of 8 cubes. If there are 4 cubes per side, there are a total of 64 cubes.

Area is x*y so it's squared. Volume is x*y*z so it's cubed. Therefore a 2x increase in dimensions means 2*2=4 increase in area and 2*2*2=8 increase in volume (and therefore mass).