The following is Tyler screen analysis of $1kg$ sample of crushed limestone$,$

$\backslash$table$[[$Mesh$,$Mass Fraction Retained$],[10,0],[14,0\mathrm{.}11],[20,0\mathrm{.}20],[24,0\mathrm{.}12],[28,0\mathrm{.}15],[32,0\mathrm{.}13],[48,0\mathrm{.}12],[$Pan$,0\mathrm{.}17]]$

If the density of limestone is $2\mathrm{.}1k\frac{g}{m^3}$ and the sphericity is $0\mathrm{.}81,$

$1-$ Plot the cumulative screen analysis.

$2-$ What is the volume$-$surface mean diameter of the sample?

$3-$ What is the specific surface area of the sample?

$4-$ what is the number of particles in the $1kg$ sample?

$5-$ What is the power required to crush $50to\frac{n}{h}r$ of the above screen analysis limestone to a size where $80\%$ of it passes $65$ mesh size?