It is proposed that the casting table be changed to produce billets of the same radius but with a flat side to allow improved stacking and handling. One of the negative impacts of this will be a reduction of mass for the proposed billet compared with the original. The figure below shows a sketch of a cross$-$section through the proposed new billet shape, a circle with a flat cast onto one side. The shaded area represents the new aluminium billet, determine:

i$.$ The height perpendicular to the flat, $h$

$11.$ The area of the shaded portion

ii$.$ The area of the unshaded area $($and hence the proportional difference in mass between the proposed billet and the existing design$)$