Perimeter and Area of Composite Figures

A factory produces circular iron discs out of rectangular iron boards of dimension of \(32\) cm by \(64\) cm. For Type A of circular iron disc, at most \(8\) of which can be produced out of one rectangular iron board, with each disc being fitted exactly in the rectangular iron board as shown in the figure below.

Find, for Type A of circular iron disc,

1. the radius, perimeter and area, respectively,
2. the area of the shaded region,
3. 
   the utilisation efficiency of the rectangular iron board, denoted by the total area of circular iron discs as a percentage of the area of the rectangular iron board. Correct your answer to \(1\) decimal place.

Another two types of circular iron discs, Type B and Type C, have radii of \(2\) cm and \(4\) cm, respectively.

4. Find the utilisation efficiency of the rectangular iron board for Type B and Type C, respectively. Correct your answer to \(1\) decimal place.
   Hence, state your finding(s) about the utilisation efficiency of Types A, B and C.

For (d), arrange Types B and C in the same rectangular rows-and-columns pattern as Type A. The efficiency comparison concerns this packing pattern, not an unrestricted maximum-packing problem. In (b), count only the shaded border gaps; the three unshaded internal gaps are excluded.