$(6$ points$)$ Particle size distribution data for a zircon $(ZrSi{O}_4)$ ceramic powder is given in the table below as determined by sieving. The data shows the weight of powder, which is captured on sieves of different sizes. Plot the histogram showing number fraction as a function of size, if density of zircon is $4\mathrm{.}7\frac{g}{c}{m}^3.$ Assume that all particles within each size interval have the same diameter equal to the midsize diameter, and that all particles are spherical.

$\begin{array}{cc}\text{S}\text{i}\text{e}\text{v}\text{e}\text{s}\text{i}\text{z}\text{e}(m)& \text{W}\text{e}\text{i}\text{g}\text{h}\text{t}on\text{s}\text{i}\text{e}\text{v}\text{e}(g)\\ 1000& 0\\ 500& 0\mathrm{.}46\\ 355& 0\mathrm{.}94\\ 250& 3\mathrm{.}10\\ 180& 5\mathrm{.}30\\ 125& 7\mathrm{.}34\\ 90& 8\mathrm{.}08\\ 63& 5\mathrm{.}00\\ 44& 3\mathrm{.}50\\ 0& 1\mathrm{.}00\end{array}$