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

Some More Questions From Areas Related to Circles Chapter

Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Draw a circle of radius 3 cm. Take two points at a distance 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

Let ABC be a right angle in which AB = 6 cm, BC = 8 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

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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. $(Use π = \frac{22}{7})$

Some More Questions From Areas Related to Circles Chapter

Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Draw a circle of radius 3 cm. Take two points at a distance 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

Let ABC be a right angle in which AB = 6 cm, BC = 8 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

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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

Some More Questions From Areas Related to Circles Chapter

Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

Draw a circle of radius 3 cm. Take two points at a distance 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

Let ABC be a right angle in which AB = 6 cm, BC = 8 cm and ∠B = 90°. BD is the perpendicular from B on AC. The circle through B, C, D is drawn. Construct the tangents from A to this circle.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

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. $(Use π = \frac{22}{7})$