A silo of $8m$ diameter and $20m$ height is loaded with food grains of density $800kg*m^{-3}.$ If the coefficient of friction and pressure ratio be $0\mathrm{.}4$ each, then what will be the lateral pressure $(kN{m}^{-2})$ when the silo is filled up to $\frac{3}{4^{th}}$ height?

$($a$)54\mathrm{.}7$

$($b$)31\mathrm{.}9$

$($c$)27\mathrm{.}4$

$($d$)47\mathrm{.}9$