Why does fine sugar has bigger suface area than rock sugar?

Question

Why does fine sugar has bigger suface area than rock sugar?

Answer 1

There are more of the smaller-surfaced granules (fine) in the same space as the bigger-surfaced granules (rock), so although each granule of fine sugar has a smaller surface area, the same weight of fine as rock sugar would have a bigger surface area due to the higher numbers.

Answer 2

Imagine any particle to be a small sphere.  (if it is a different shape doesn't matter much - in principle the following still applies)

surface area of particle is proportional to r^2 i.e. = A.r^2

volume of particle is proportional to r^3   i.e. =B.r^3 where r is the particle's radius and A and B are constants.

therefore the ratio [surface area] / [volume] =C/r where C=A/B

in other words, as the radius of particles decreases their surface area to volume ratio increases i.e very small size particles have much higher ratios of surface area to volume than larger particles.

This relationship is given by nature and applies to particles of any substance.

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