In the figure (i) given below, AC and BD are two perpendicular diameters of a circle ABCD. Given that the area of shaded portion is 308 cm², calculate :

(i) the length of AC and

(ii) the circumference of the circle.

(i) Let r be the radius of the circle. We know that,

Diameters of the circle divide circle into 4 equal quadrants.

Hence, area of each quadrant = $\dfrac{1}{4}$ πr².

Since, 2 quadrants are shaded.

∴ Area of shaded region = $2 \times \dfrac{1}{4}$ πr²

⇒ 308 = $\dfrac{1}{2} \times \dfrac{22}{7}$ r²

⇒ r² = $\dfrac{308 \times 14}{22}$

⇒ r² = 14 × 14 = 196

⇒ r = $\sqrt{196}$ = 14 cm.

Since, AC is the diameter of circle so,

⇒ AC = 2r = 28 cm.

Hence, AC = 28 cm.

(ii) Circumference of circle = 2πr

= $2 \times \dfrac{22}{7} \times 14$

= 88 cm.

Hence, circumference of circle = 88 cm.