Area of Sector

Q. The length of the minute hand of a wall clock is 7 cm, then area swept by the minute hand in 10 minutes is ____ (use $\pi$ =$\frac{22}{7}$)

1. 30 ${cm}^2$
2. 30.66 ${cm}^2$
3. 28.69 ${cm}^2$
4. 25.66 ${cm}^2$

Q. In fig.4, O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region. (Take $\pi =3.14$)

Q.

Define Sector of a Circle

Q.

A circle has two parallel chords of lengths 6 cm and 8 cm. If the chords are 1 cm apart and the center is on the same side of the chords, then diameter of the circle is of length

1. 5 cm

2. 6 cm

3. 8 cm

4. 10 cm

Q.

There is a circle of diameter 10 cm. A chord of length 6 cm is drawn inside the circle. What is the distance between the centre and this chord in cm?

1. 4

2. 2

3. 3

4. 1.5

Q. Calculate the area of the shaded region in the given figure, common between the two quadrants of the circles of radius 10 cm each.
(use $\pi$ = 3.14)

1. 58 ${cm}^2$
2. 60 ${cm}^2$
3. 57 ${cm}^2$
4. 67 ${cm}^2$

Q. The length of an arc which subtends an angle $\theta$ at the centre of a circle of radius r is

1. $\frac{\mathrm{\pi r\theta }}{180}$
2. $\frac{\mathrm{\pi r\theta }}{360}$
3. $\frac{\mathrm{\pi r\theta }}{90}$
4. $\frac{\mathrm{\pi r\theta }}{60}$

Q.

Question 3
Find the area of the shaded region in Fig. 12.21, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

Q.

Question 126 (b)

Architects design many types of buildings. They draw plans for houses, such as the plant shown in the following figure.

An architect wants to install a decorative moulding around the ceilings in the rooms. The decorative moulding costs ₹ 500/ meter.

The carpet costs ₹ 200 per $m^2$. Find the cast of carpeting each room.

Q.

A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of ${120}^{\circ }$. Find the total area cleaned at each sweep of the blades. (use $\pi$ = $\frac{22}{7}$)

1. 1750.5 ${cm}^2$
2. 1600 ${cm}^2$
3. 1450.9 ${cm}^2$
4. 1309.5 ${cm}^2$

Q. Find the area of sector, whose radius is 5 cm, subtending an angle of ${60}^{\circ }$.

1. 13.09 ${cm}^2$
2. 14.5 ${cm}^2$
3. 17 ${cm}^2$
4. 16.5 ${cm}^2$

Q. The part of a circle enclosed by two radii of a circle is called ______ of a circle.

1. sector
2. diameter
3. segment
4. area

Q. Question 2
Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and $\angle AOC={40}^{\circ }$.

Q.

The area in $c{m}^2$ of the shaded region if the radius of the smaller circles are 1 cm each is 6.28 $c{m}^2$.

1. True

2. False

Q.

A drain cover is made from a square metal plate of side 40 cm and has 336 holes of radius 1 cm each drilled in it. Find the area in ${\text{cm}}^2$ of the remaining square plate.
(Take $\pi$ =$\frac{22}{7}$)

1. 253

2. 544

3. 636

4. 564

Q. Given figure depicts a racing track whose left and right ends are semi-circular. The distance between the two inner parallel line segments is 60 $m$ and they are each 106 $m$ long. If the track is 10 $m$ wide, find the area of the track (in $m^2$).

1. 4320 $m^2$
2. 2340 $m^2$
3. 5000 $m^2$
4. 4320 $m^2$

Q. In the given figure, AB is a chord of length 6 cm drawn in a circle with centre 'O'. If OM is the perpendicular bisector of length $\sqrt{27}$ cm to chord AB then, find the area of sector of OAYB. (Use $\pi$=$\frac{22}{7}$)

1. 19.65 ${cm}^2$
   
2. 15.23 ${cm}^2$
   
3. 12.36 ${cm}^2$
   
4. 18.85 ${cm}^2$
   

Q.

A cow is tied to a pole fixed at one corner of a 20 m $\times$ 20 m square agricultural field by a 10 m long rope. Find the area of that part of the field in which the cow cannot graze. (Take $\pi =3.14$)

1. 221.5 $m^2$
2. 350 $m^2$
3. 321.5 $m^2$
4. 400 $m^2$

Q.

I have thin matchsticks each of thickness 1 mm. The length of each matchstick is ‘L ’ mm. There are a few matchsticks kept side by side on a table such that the heads of all matchsticks are in one line and the tail ends of all matchsticks are together in another different line and the lengths of the matchsticks are parallel. The number of matchsticks kept is ‘B’. What is the area of the plane formed by the matchsticks (in ${mm}^2$)?

Q.

Draw a map of your class room using proper scale and symbols. There are 20 tables in the class room arranged in two columns and two windows are located at the center of two side of rectangular class. Dimension of a class room is $8m\times 4m$, Dimension of a table $1.5m\times 1m$. Dimension of window $3m\times 2m$. [4 MARKS]

Q.

Calculate the area of the shaded region in the figure given in $c{m}^2.$

1. 469.3

2. 281.2

3. 1120.4

4. 2499.7

Q. In the figure below, AB and CD are two diameters of a circle (with center O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

1. 65.5 $c{m}^2$
2. 66.5 $c{m}^2$
3. 67.5 $c{m}^2$
4. 68.5 $c{m}^2$

Q. The length of an arc is 35m. If the radius of the circle is 14m, find the angle subtended by the arc.

Q.

The area of a sector with radius 14 cm is 154 $c{m}^2$. The central angle of the sector (in degrees) is

1. 90${}^{\circ }$

2. 180${}^{\circ }$

3. 45${}^{\circ }$

4. 270${}^{\circ }$

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.

1. $5c{m}^2$

2. $6c{m}^2$

3. $8c{m}^2$

4. $10c{m}^2$

Q. If the degree measure of the angle at the center is 1, the area of the sector with radius r = 1 will be.

1. $\frac{\pi }{360}$
2. $\pi$
3. 180$\pi$

Q. Find the radius of the sector which is making an angle of ${60}^{\circ }$ and has an area of 924 ${cm}^2$. (use $\pi$ = $\frac{22}{7}$)

1. 42 cm
2. 32 cm
3. 52 cm
4. 50 cm

Q. Direction: In the following question, a statement of assertion (A) is followed by a statement of reason (R).
Mark the correct choice as:

Assertion: In a circle of radius 6cm, the angle of sector is 60°. The area of the sector is $18\frac{6}{7}c{m}^2$.

Reason: The circumference of a circle with radius $r$ is $2\pi r$.

1. Both assertion (A) and reason (R) are false

2. Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A)..

3. Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
   

4. Assertion (A) is true but reason (R) is false.

Q. The perimeter of a quadrant of a circle of radius $\frac{7}{2}$ cm is:

1. $5.5cm$
2. $3.5cm$
3. $7.5cm$
4. $12.5cm$

Q.

The area in $c{m}^2$ of a sector of a circle with radius 6 cm if angle of the sector is ${60}^{\circ }$ is _________

1. 19.5

2. 20.1

3. 25.9

4. 18.8