# Area of a Sector

## Trending Questions

**Q.**

Area of a sector of angle p (in degrees) of a circle with radius r is

× 2πr

× 2πr

× π

× 2π

**Q.**Question 5

From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in Fig. 12.23. Find the area of the remaining portion of the square.

**Q.**

What's the geometric proof of a2-b2

**Q.**

The length of the minute hand of a clock is 14 cm. The area swept by the minute hand between 3:20 and 3:45 is

256.66 cm2

2.566 cm2

2560 cm2

0.2566 cm2

**Q.**

Identify the major sector and minor segment in the given figure:

OACBO, OADB

OACBO, ADBA

ABDA, ACBA

OADBO, ACBA

**Q.**

Find the area of the sector in a clock swept by the minute hand in five minutes if the radius is 14 cm.

(Take π as 227)

616 cm2

- 51.33 cm2
- 42 cm2
- None of the above

**Q.**Question 2 (v)

Write True or False: Give reasons for your answers.

(v) Sector is the region between the chord and its corresponding arc.

**Q.**Find the area of the shaded region

- 62cm2
- 57cm2
- 38cm2
- 43cm2

**Q.**

Imagine a picture of a scoop of ice-cream in a cone. Consider the cone to be in equilateral shape and the scoop to fit at the top of the cone. What would be the area of the picture if the side of the equilateral triangle is, a = 6 cm?

29.71 cm

^{2}27.98 cm

^{2}25.31 cm

^{2}32.45 cm

^{2}

**Q.**

The window is shown in the shape of a semi-circle with radius 4 ft. The distance from S to T is 2 ft and the measure of arc AB=45∘. Area of the glass in the region ABCD is

4.7 sq. ft

4.9 sq. ft

4.5 sq. ft

5 sq. ft

**Q.**

The shaded region consists of a chord and the arcs of the circle. The region in the yellow has the major arc so it is the major segment and the purple region consists of the minor arc so it is the minor segment.

Yellow –Major segment , Purple –Minor segment

Purple –Major segment, Yellow –Minor segment

Either A or B

None of these

**Q.**Match the following with the area of shaded regions in cm2.

- 250Ï€3
- 50Ï€3âˆ’25âˆš3
- 50Ï€3

**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 arc P is

51.2 cm2

52.3 cm2

53.4 cm2

54.5 cm2

**Q.**Choose the major sector in the given figure.

**Q.**

OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region.

**Q.**

A circle of radius $2cm$ is cut out from a square piece of an aluminium sheet of side$6cm$. What is the area of the left over aluminium sheet? (Take $\mathrm{\xcf\u20ac}=3.14$)

**Q.**

Compare area of region I and II.

- \N
- \N
- True
- False

**Q.**

The ________ of a circle has the major arc as part of its boundary.

Major sector

Minor sector

Minor Segment

Major segment

**Q.**

A polygon is drawn inside a circle of radius 7 cm.

What is the area of the shaded region (in cm2) if the area of the polygon is 24picm2?

24π cm2

25π cm2

49π cm2

7π cm2

**Q.**

In the figure, there is a jogging track which consists of two semi-circular track and two rectangle track that have to be renovated. For the circular parts, the inner and outer radii are 6 m and 8 m respectively. Find the area highlighted in green colour (in square meters).

22

44

66

88

**Q.**

Find the area of the sector in a clock swept by the minute hand in five minutes if the radius is 14 cm.

(Take π as 227)

616 cm2

- 51.33 cm2
- 42 cm2
- None of the above

**Q.**

AB is the chord of the given circle. Name the regions in yellow and purple.

Purple –Major segment, Yellow –Minor segment

None of these

Either A or B

Yellow –Major segment , Purple –Minor segment

**Q.**

Find the area of the shaded region in Fig, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.

(36√3+6607)cm2

(32√3+6607)cm2

(36√3+5507)cm2

(36√3+6609)cm2

**Q.**

The shaded region consists of a chord and the arcs of the circle. The region in the yellow has the major ar so it is the major segment and the purple region consists of the minor arc so it is the minor segment.

**Q.**

Find the area of the shaded region where ABC is a quadrant of radius 5 cm and a semicircle is drawn with BC as diameter.

12.5 cm2

7.14 cm2

19.64 cm2

8.8 cm2

**Q.**

The adjacent figure shows two arcs P and Q. Arc P is part of the circle with centre O and radius OA=10 cm. Arc Q is a part of the circle with centre M and radius AM=5 cm, where M is the mid-point of AB. Area enclosed by the arc P and chord, AB is

25√3−50π3 cm2

50π3+25√3 cm2

50π3−25√3 cm2

None of these

**Q.**

Find the area of the shaded region (in cm2) as shown in figure of the two concentric circles with centre O and radius 7 cm and 14 cm respectively. Given ∠AOC = 40∘.

(use π = 227)

42.1 cm2

51.32 cm2

67.8 cm2

96.5 cm2

**Q.**Tick the correct answer in the following:

Area of a sector of angle p (in degrees) of a circle with radius R is

**Q.**

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 m2).

**Q.**Simplify : 3√48−52√13+4√3