compare ratio of particle surface area to volume?

Question

Colloidals are stablilized by maximizing the surface area in contact with the surrounding liquid relative to the volume of the nanoparticle. compare the ratio of the particle surface area (in nm^3) for nanospheres having diameters of (a) 20nm and (b) 100nm. The volume and surface area of a sphere can be calculated from the equations below. Nanospheres of which size would form the most stable colloid?

Area=4pie r^2 Volume= 4/3pie r^3

Answer 1

For 20nm particle;
A = 1256 nm^2
V = 4187 nm^3
A / V = 0.3

For 100nm particle;
A = 3.14e4 nm^2
V = 5.23e5 nm^3
A / V = 0.06

The smaller particle (20nm) will have
a greater surface area per volume.