In the figure (ii) given below, the area enclosed between the circumferences of two concentric circles is 346.5 cm². The circumference of the inner circle is 88 cm. Calculate the radius of the outer circle.

Let radius of inner circle = r cm.

Circumference = 2πr

⇒ 88 = 2πr

⇒ r = $\dfrac{88}{2π}$

⇒ r = $\dfrac{44}{π}$

⇒ r = $\dfrac{44}{\dfrac{22}{7}} = \dfrac{44 \times 7}{22}$

⇒ r = 2 × 7 = 14 cm.

Let radius of outer circle = R cm.

From figure,

Area of shaded region = Area of outer circle - Area of inner circle

⇒ 346.5 = π(R)² - πr²

⇒ 346.5 = π(R)² - π(14)²

⇒ 346.5 = π(R² - 196)

⇒ R² - 196 = $\dfrac{346.5}{π}$

⇒ R² - 196 = $\dfrac{346.5}{\dfrac{22}{7}}$

⇒ R² - 196 = $\dfrac{346.5 \times 7}{22}$

⇒ R² - 196 = 110.25

⇒ R² = 110.25 + 196

⇒ R² = 306.25

⇒ R = $\sqrt{306.25}$

⇒ R = 17.5 cm

Hence, radius of outer circle = 17.5 cm.