An engine develops $30$ KW at $1250re\frac{v}{m}in.$ The engine is fitted with a cone clutch whose cone face angle is $12\mathrm{.}5$ and the mean diameter is $400$ mm $.$ If the coefficient of friction is $0\mathrm{.}3$ and the normal mean pressure is $0\mathrm{.}08\frac{N}{m}{m}^2,$ assuming uniform wear, determine:

$($i$)$ The axial force required.

$($ii$)$ Outer and inner radii of the clutch.