In Fig., AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. OB is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region. $|Use π = \frac{22}{7}|$

Solution

$AB and CD are the diameters of a circle with centre O . ∴ OA = OB = OC = 7 cm (Radius of the circle) Area of the shaded region = = Area of the circle with diameter OB + (Area of the semi - circle ACDA - Area of ∆ ACD) = π {(\frac{7}{2})}^{2} + (\frac{1}{2} x π x 7^{2} - \frac{1}{2} x CD x OA) = \frac{22}{7} x \frac{49}{4} + \frac{1}{2} x \frac{22}{7} x 49 - \frac{1}{2} x 14 x 7 = \frac{77}{2} + 77 - 49 = 66.5 {cm}^{2}$

Some More Questions From Areas Related to Circles Chapter

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Areas Related To Circles

In Fig., AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. OB is the diameter of the smaller circle. If OA = 7 cm, 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°.

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Areas Related To Circles

In Fig., AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. OB is the diameter of the smaller circle. If OA = 7 cm, 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°.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

In Fig., AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. OB is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region. $|Use π = \frac{22}{7}|$