Sample: How to calculate mass of nanopaticles with given density and Vol %
Defining the following


Density of solution: $\rho = \pu{1.18 g/cc}$
Density of water: $\rho_w$
Density of nanoparticles: $\rho_{np}$
% (v/v) n.p.s: $p_v=3.9$%
% (w/w) n.p.s: $p_{wt}$


Then solve for $\rho_{np}$ in the following equation (you'll need to look up missing value of water density):

$$\rho = \frac{p_v}{100}\rho_{np} + \frac{100-p_v}{100}\rho_{h2o}$$

With $\rho_{np}$ you can compute $p_{wt}$

$$p_{wt} = 100\frac{p_{v}\rho_{np}}{p_{v}\rho_{np}+(100-p_{v})\rho_{w}}$$

As noted in the comments, the resulting density of the particles ignores the effect of the added cationic surfactant. Also, the solvent density is assumed that of water, free (not particle bound) detergent or other additives assumed to be negligible.