P6 / Rosyth / 2020 / SA2 Prelims / Paper 2 – Q14 [4 marks]

Question:

The figure below shows a rectangle and 11 identical shaded circles. Each shaded circle is in contact with those next to it. The rectangle has a perimeter of 384 cm.
a) Find the radius of one circle.
b) More identical shaded circles are added. The whole rectangle is then covered with the maximum number of shaded circles. Find the area of the rectangle that is not covered by the shaded circles.
(Take π = 22/7)

Solution: