The areas of two concentric circles are 962.5 cm² and 1386 cm² respectively. Find the width of the ring.

Let radius of smaller circle be r cm and radius of bigger circle be R cm.

Given

Area of smaller circle = 962.5 cm²

Area of bigger circle = 1386 cm²

Width of ring = R − r

Area of bigger circle = πR²

$\Rightarrow 1386 = \dfrac{22}{7} \times R^2 \\[1em] \Rightarrow R^2 = \dfrac{1386 × 7}{22} \\[1em] \Rightarrow R^2 = \dfrac{9702}{22} \\[1em] \Rightarrow R^2 = 441 \\[1em] \Rightarrow R = \sqrt{441} \\[1em] = 21 \text{ cm}.$

Calculating the area of smaller circle,

$\text{Area of smaller circle} = πr^2 \\[1em] \Rightarrow 962.5 = \dfrac{22}{7} r^2 \\[1em] \Rightarrow r^2 = \dfrac{962.5 × 7}{22} \\[1em] \Rightarrow r^2 = \dfrac{6737.5}{22} \\[1em] \Rightarrow r^2 = 306.25 \\[1em] \Rightarrow r = \sqrt{306.25} \\[1em] = 17.5 \text{ cm}.$

Width of the ring = R - r

= 21 - 17.5 = 3.5 cm.

Hence, width of the ring = 3.5 cm.