In the given figure, the area enclosed between two concentric circles is 808.5 cm². The circumference of the outer circle is 242 cm. Calculate :

(i) the radius of the inner circle,

(ii) the width of the ring.

Let R be the radius of outer circle and r be the radius of inner circle.

(i) Given,

Circumference of outer circle = 242 cm.

$\therefore 2πR = 242 \\[1em] \Rightarrow 2 \times \dfrac{22}{7} \times R = 242 \\[1em] \Rightarrow \dfrac{44}{7} \times R = 242 \\[1em] \Rightarrow R = \dfrac{242 × 7}{44} \\[1em] = 38.5 \text{ cm}.$

Area enclosed between two concentric circles = Area of bigger circle - Area of smaller circle

= πR² - πr²

= π(R² - r²)

Given,

Area enclosed between two concentric circles = 808.5 cm²

⇒ 808.5 = $\dfrac{22}{7}$ (R² - r²)

⇒ (38.5)² - r² = $\dfrac{808.5 × 7}{22}$

⇒ 1482.25 - r² = $\dfrac{5659.5}{22}$

⇒ 1482.25 - r² = 257.25

⇒ r² = 1482.25 - 257.25

⇒ r² = 1225

⇒ r = $\sqrt{1225}$ = 35 cm.

Hence, radius of inner circle = 35 cm.

(ii) Width of ring = R - r

= 38.5 - 35

= 3.5 cm.

Hence, width of the ring = 3.5 cm.