Area of Segment

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. AB and CD are two chords of a circle such that AB = 6 cm, CD = 12 cm and $AB\parallel CD$. If the distance between AB and CD is 3 cm, find the radius of the circle. [4 MARKS]

Q.

It is proposed to add to a square lawn with each side $58m$ two circular ends the center of each circle being the point of intersection of the diagonals of the square. The area of the whole lawn is ?

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 $70c{m}^2$.

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.

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.

1. 2

2. 1.5

3. 3

4. None of these

Q. Find the area of the shaded region in figure, where radii of the two concentric circles with centre O are $7$cm and $14$cm respectively and $\angle AOC={40}^o$.

1. $10.67c{m}^2$
2. $410.67c{m}^2$
3. None of these
4. $40.67c{m}^2$

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

Q.

The radius of the circle given above is 7cm and the angle subtended by the arc is ${60}^{\circ }$.
If the area of $\Delta$OAB is $21{cm}^2$, then find the area of segment APBA.
$(\pi =\frac{22}{7})$

1. $5.8{cm}^2$

2. $4.7{cm}^2$

3. $8{cm}^2$

4. $1{cm}^2$

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. Question 6

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

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. 180

2. 60

3. 90

4. 120

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.

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

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