Average diameters of colloids

A dispersion of spherical polymer particles contains Np = 4•1013 particles/dm3. The total surface of the particles in 1 dm3 is Asp = 820 m2.

a) What kind of average diameter can we calculate. Calculate this average diameter.

b) If we know that the dispersion contains 60 vol% water, we can calculate another type of average diameter. Which? Find it!

a) Surface average.

$$\bar{d_s} = \sqrt{\frac{\Sigma n_i d_i^2}{\Sigma n_i}}$$

b) Volume average.

$$\bar{d_s} = \sqrt{\frac{\Sigma n_i d_i^3}{\Sigma n_i}}$$

I don't know how to incorporate the data into the formulas.
 Can't you just work it out by taking the surface area of a sphere and working back to get the radius? You know the total surface area of the total particles in 1 litre, and you know how many particles there are in 1 litre, so from that you can work out the surface area of 1 particle.
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