Area of a Segment

Q. Question 1
AD is a diameter of a circle and AB is a chord. If AD = 34cm, AB = 30cm, the distance of AB from the centre of the circle is

(A) 17 cm
(B) 15 cm
(C) 4 cm
(D) 8 cm

Q.

In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.

1. 98.01

2. 98.01 $m^2$
3. 89.01 $c{m}^2$
4. 9801 $m{m}^2$

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. $441\sqrt{3}sqcm$

2. $1743sqcm$

3. $4620+441\sqrt{3}sqcm$

4. $5544sqcm$

Q.

Area of major segment = Area of circle - Area of minor segment.

1. True

2. False

Q. In the figure given below, the radius of the circle is 84 cm. The angle in the sector is ${60}^{\circ }$​. What is the area of the minor segment APB?

1. $3696+1764\sqrt{3}{cm}^2$
2. $18480+1764\sqrt{3}{cm}^2$
3. $3696{cm}^2$
4. $3696-1764\sqrt{3}{cm}^2$

Q. In a circle, the part between a chord and the arc having the chord is called segment.

1. True
2. False

Q.

Question 6

In the figure given, the radius of the circle is 15cm. The angle subtended by the chord AB at the centre O is ${60}^{\circ }$. Find the area of the major and minor segments.

Q.

Area of major segment = Area of circle - Area of minor segment.

1. False

2. True

Q.

In fig, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.

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)

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

Q.

There is a circle with radius 6 cm. A chord is drawn in it. Find the angle subtended by the minor segment of the chord at the centre of the circle if the area of segment is 22.1 ${cm}^2$.

1. 60

2. 90

3. 180

4. 120

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. - 2ab

3. -(ab)

4. - (ab)

Q. The adjacent figure shows two arcs P and Q. Arc P is part of the circle with centre O and radius OA. Arc Q is a part of the circle with centre M and radius AM, where M is the mid-point of AB. Area enclosed by the arcs P and Q is

1. $(\sqrt{3}-25\frac{\pi }{4})c{m}^2$
2. $(25\sqrt{3}-\frac{\pi }{4})c{m}^2$
3. $25(\sqrt{3}-\frac{\pi }{6})c{m}^2$
4. None of these

Q.

Question 7
A chord of a circle of radius 12 cm subtends an angle of ${120}^{\circ }$ at the center. Find the area of the corresponding segment of the circle. (Use $\pi =3.14and\sqrt{3}=1.73)$

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

Q.

In figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region (in $c{m}^2$).

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

1. 
2. 
3. 
4. 

Q.

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

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

Q.

A circumcircle is drawn around an equilateral triangle. If the circum-radius r = 14 cm, find the area of the shaded region.

1. 61.68 cm²

2. 65.32 cm²

3. 69.51 cm²

4. 64.23 cm²

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. $441\sqrt{3}sqcm$

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

3. $1743sqcm$

4. $924sqcm$