Area of a Segment of a Circle

Q.

A circle having radius 4 cm contains a chord of length 4 cm and subtends an angle of 60 degrees. Find the area of the minor segment of the chord. [Take π = 22/7 and √3=1.73]

1. $2c{m}^2$

2. $1.46c{m}^2$

3. $0.5c{m}^2$

4. $3c{m}^2$

Q.
In the given figure, a semicircle is drawn on the hypotenuse of the right-angled triangle. Another arc of radius 30 cm is drawn passing through A and C with O as the center. What is the area of the shaded region? (Take $\pi$ as 3.14 and $\sqrt{3}$ = 1.732)

1. 117.75 sq cm
2. 271.95 sq cm
3. 216 sq cm
4. 108 sq cm

Q. Two circles intersect as shown in the diagram below. The radii of the circles are 14cm each and $\angle AOP={45}^{\circ }$​ What is the area of the region shaded in blue?

1. $132.5\pi sq.cm$
2. $112sq.cm$
3. $156sq.cm$
4. $56sq.cm$

Q. In the figure given below, the radius of the circle is 42cm. The angle in the sector is ${60}^{\circ }$​. What is the area of the segment APB?

1. $924sqcm$
2. $441\sqrt{3}sqcm$
3. $1743sqcm$
4. $924-441\sqrt{3}sqcm$

Q.

Find the area of the minor segment of a circle if the area of the circle is $100c{m}^2$ and the area of the major segment is $70c{m}^2$.

1. $170c{m}^2$

2. $130c{m}^2$

3. $30c{m}^2$
4. $200c{m}^2$

Q.

In the figure given below, the radius of the circle is 42 cm. The angle in the sector is ${60}^{\circ }$​. What is the area of the major segment?

1. 5544 sq. cm

2. $441\sqrt{3}$ sq. cm

3. $4620+441\sqrt{3}$ sq. cm

4. 1743 sq. cm

Q.

Area of the shaded portion in the following figure is equal to area of .
.

1. \N
2. \N
3. False
4. True

Q.

A circular garden of radius 10 m is divided into two parts by a straight line fence. Smaller part is the walking area and flowers are planted in the larger part. The fence is at a distance of 6 m from the centre of the garden. What is the walking area in $m^2$? It is given that cos 53°= $\frac{3}{5}.$

1. $36m^2$

2. $44.5m^2$

3. $12m^2$

4. $72m^2$

Q.

A chord of a circle of radius 12 cm subtends an angle of ${120}^{\circ }$ at the centre. Find the area in $c{m}^2$ of the corresponding segment of the circle. (Use $\pi$ = 3.14 and $\sqrt{3}$ = 1.73)

___

Q.

In the given diagram, find the area of segment PRQS. Sides OS and SQ have lengths a and b respectively. Let the area of circle be A.

1. - ab

2. -(ab)

3. - (ab)

4. - 2ab