Sector of a Circle

Q. In fig. 6, find the area of the shaded region, enclosed between two concentric circles of radii 7 cm and 14 cm where $\angle AOC={40}^{\circ }$. (Use $\pi =\frac{22}{7}$)

Q.

Define Major Segment of a Circle.

Q. What is a locus

Q. In fig., arcs are drawn by taking vertices A, B and C of an equilateral triangle of side 10 cm, to intersect the sides BC, CA and AB at their respective mid-points D, E and F. The area of the shaded region is _____. (Use $\pi =3.14$).

1. $37.25c{m}^2$
2. $38.25c{m}^2$
3. $39.25c{m}^2$
4. $40.25c{m}^2$

Q.

Sector is the region between the chord and its corresponding arc. Write True or False. Give reason for your answer

1. True
2. False

Q.

The perimeter of a certain sector of a circle of radius$5.6\mathrm{m}$ is$27.2\mathrm{m}$. Find the area of the sector.

Q. A chord PQ of a circle with radius 6 cm subtends an angle of ${60}^o$ with the centre of the circle. The area of the minor and the major segment are _____ and _____ respectively.
(Use $\pi =3.14,\sqrt{3}=1.73$ )

1. $3.27c{m}^2,113.04c{m}^2$
   
2. $113.04c{m}^2,3.27c{m}^2$
3. $3.27c{m}^2,109.77c{m}^2$
4. $109.77c{m}^2,3.27c{m}^2$

Q.

The longest chord of a circle is $18\text{cm}$. What is the radius of the circle?

Q. The length of the hour hand of a clock is 7cm. Find the area swept by the hour hand during the time 6:00AM to 6:45 AM

Q.

A solid figure with only $1$ vertex is a

Q. In the given figure, A is the centre of the circle. $\angle ABC={45}^o$ and $AC=7\sqrt{2}cm.$ Find the area of segment BXC. (Use $\pi =\frac{22}{7}$ )

1. $27c{m}^2$
2. $28c{m}^2$
3. $29c{m}^2$
4. $26c{m}^2$

Q. The area of a circle circumscribing a square of side 14 cm is:
(Take π = $\frac{22}{7}$)

[1 mark]

1. $308c{m}^2$
2. $408c{m}^2$
3. $154c{m}^2$
4. $204c{m}^2$

Q.

The diameter of a tyre of a tricycle is $32\text{cm}$. What is the radius of the tyre ?

Q. Chord PQ of a circle of radius 6 cm subtends an angle of ${60}^o$ at the centre O. Find the area of the minor segment and major segment respectively.
(Use $\pi =3.14,\sqrt{3}=1.73$ )

1. $3.27c{m}^2,113.04c{m}^2$
   
2. $113.04c{m}^2,3.27c{m}^2$
3. $3.27c{m}^2,109.77c{m}^2$
4. $109.77c{m}^2,3.27c{m}^2$

Q.

A circle of radius $3cm$ can be drawn through two points $A,B$ such that$AB=6cm$. Write True or False and justify your answer in each of the following:

1. True
2. False

Q.

A sector of angle $40°$ is cut out from a circle. If the area of the sector is $\frac{77}{18}{\mathrm{m}}^2$, find the radius of the circle.

Q. Q29. The length of the hour hand of a clock is 7cm. Find the area swept by the hour hand during the time 6:00I4\rbrack AM to 6:45 AM.

Q. A set of points equidistant from a fixed point in a plane figure is called

1. circle
2. none of these
3. square
4. triangle

Q. The region bounded by the major arc and radii is called the.

1. major sector
2. minor sector
3. major segment
4. minor segment

Q. In the given figure, O is the centre of the sector. $\angle ROQ=\angle MON={60}^o.$ OR = 7 cm, and OM = 21 cm. The sum of the lengths of arc RXQ and arc MYN is _____. (Use $\pi =\frac{22}{7}$ )

1. 7.33 cm
   
2. 22 cm
3. 29.33 cm
4. 36.66 cm

Q. Choose the major sector in the given figure.

1. 
2. 
3. 

Q. The areas of the major and the minor sector of a circle are equal when the central angle is .

1. ${90}^{\circ }$
2. ${180}^{\circ }$
3. ${60}^{\circ }$

Q. Question 9
The area of two sector of two different circles with equal corresponding arc lengths are equal . Is this statement true ? why?

Q. The geometric shape that has no corners is _____.

1. square
2. rectangle
3. circle
4. hexagon

Q. Area of sector whose radius is 14 cm and length of its corresponding arc is 20 cm is

Q.

A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of ${115}^{\circ }$. Find the total area in $c{m}^2$ cleaned at each sweep of the blades. [2 MARKS]

Q. Find the area of the shaded region in the given figure $BC=BD=8cm$, $AC=AD=15cm$ and $O$ is the centre of the circle (Take $\pi =3.14)$

Q. The areas of the major and the minor sector of a circle are equal when the central angle is .

1. ${90}^{\circ }$
2. ${180}^{\circ }$
3. ${60}^{\circ }$

Q. In the given figure, O is the centre of the sector. $\angle ROQ=\angle MON={60}^o.$ OR = 7 cm, and OM = 21 cm. The sum of the lengths of arc RXQ and arc MYN is _____. (Use $\pi =\frac{22}{7}$ )

1. 7.33 cm
   
2. 22 cm
3. 29.33 cm
4. 36.66 cm

Q.

Find the area of a shaded region in the Fig. where a circular arc of radius 7 cm has been drawn with vertex A of an equilateral triangle ABC of side 14 cm as centre. (Use $pi=\frac{22}{7}$ and $\sqrt{3}=1.73$)

(2 marks)