Project ForgeThe figure shows an annular ring with outer and inner radii b and a, respectively. The annular space has been painted in the form of blue-coloured circles touching the outer and inner periphery of the annular space. If the maximum n number of such circles can be painted, the unpainted area available in the annular space is _____.
- π[(b²−a²) − (n/4)(b−a)²]
- Bπ[(b²−a²) − n(b−a)²]
- Cπ[(b²−a²) + (n/4)(b−a)²]
- Dπ[(b²−a²) + n(b−a)²]
Explanation
The annulus has area π(b²−a²). Each painted circle touches both the inner and outer boundary of the annular ring, so its diameter equals the ring's width (b−a), giving each circle a radius of (b−a)/2 and area π(b−a)²/4. With n such circles painted, total painted area = nπ(b−a)²/4. Unpainted area = π(b²−a²) − nπ(b−a)²/4 = π[(b²−a²) − (n/4)(b−a)²].
Source: GATE CS 2020 (2020)
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