Question

In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region. $(Use π = \frac{22}{7})$

Solution

We have,

Area of the region ABCD

= Area of the sector AOB - Area of the sector COD

$= (\frac{60}{360} x \frac{22}{7} x 42 x 42 - \frac{60}{360} x \frac{22}{7} x 21 x 21) {cm}^{2} = (\frac{1}{6} x 22 x 6 x 42 - \frac{1}{6} x 22 x 3 x 21) {cm}^{2} = (22 x 42 - 11 x 21) {cm}^{2} = (924 - 231) {cm}^{2} = 693 {cm}^{2} Area of circular ring = (\frac{22}{7} x 42 x 42 - \frac{22}{7} x 21 x 21) {cm}^{2} = (22 x 6 x 42 - 22 x 3 x 21) {cm}^{2} = (5544 - 1386) {cm}^{2} = 4158 {cm}^{2}$

Hence, Required shaded region = Area of circular ring - Area of region ABCD

= (4158 - 693) cm²

= 3465 cm²

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In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region. $(Use π = \frac{22}{7})$

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Areas Related To Circles

In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region. Use π = 227

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In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If ∠AOB = 60°, find the area of the shaded region. $(Use π = \frac{22}{7})$