Discussion
Three circles of radius 3.5 cm are placed in such a way that each circle touches the other two. The area of the portion enclosed by the circles is
Answer: A
The centres of the three circles form an equilateral triangle of side 7 cm, whose area is \(\tfrac{\sqrt{3}}{4}\times 49\approx 21.217\) cm\(^2\). The three circles cover three 60 degree sectors, together half a circle: \(\tfrac{1}{2}\pi r^{2}\).
With \(\pi=\tfrac{22}{7}\) this is \(\tfrac{1}{2}\times\tfrac{22}{7}\times12.25=19.25\). The enclosed area is \(21.217-19.25\approx1.967\) cm\(^2\), option A.
With the exact value of \(\pi\) the result is 1.975, which is printed as option B, so the key assumes \(\pi=\tfrac{22}{7}\), the usual choice with a radius of 3.5.
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