Area of a Sector

Q.

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

1. × 2πr

2. × 2πr

3. × π

4. × 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 $14cm.$ The area swept by the minute hand between $3:20$ and $3:45$ is

1. $256.66c{m}^2$

2. $2.566c{m}^2$

3. $2560c{m}^2$

4. $0.2566c{m}^2$

Q.

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

1. OACBO, OADB

2. OACBO, ADBA

3. ABDA, ACBA

4. 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.

$\left(Take\pi as\frac{22}{7}\right)$

1. $616c{m}^2$

2. $51.33c{m}^2$
3. $42c{m}^2$
4. 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

1. 62cm${}^2$
2. 57cm${}^2$
3. 38cm${}^2$
4. 43cm${}^2$

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?

1. 29.71 cm²

2. 27.98 cm²

3. 25.31 cm²

4. 32.45 cm²

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 $AB={45}^{\circ }$. Area of the glass in the region $ABCD$ is

1. 4.7 sq. ft

2. 4.9 sq. ft

3. 4.5 sq. ft

4. 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.

1. Yellow –Major segment , Purple –Minor segment

2. Purple –Major segment, Yellow –Minor segment

3. Either A or B

4. None of these

Q. Match the following with the area of shaded regions in $c{m}^2$.

1. $\frac{250\pi }{3}$
2. $\frac{50\pi }{3}-25\sqrt{3}$
3. $\frac{50\pi }{3}$

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

1. $51.2c{m}^2$

2. $52.3c{m}^2$

3. $53.4c{m}^2$

4. $54.5c{m}^2$

Q. Choose the major sector in the given figure.

1. 
2. 
3. 

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 $\pi =3.14$)

Q.
Compare area of region I and II.

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

Q.

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

1. Major sector

2. Minor sector

3. Minor Segment

4. Major segment

Q.

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

What is the area of the shaded region (in $c{m}^2)$ if the area of the polygon is 24$pi{cm}^2$?

1. $24\pi c{m}^2$

2. $25\pi c{m}^2$

3. $49\pi c{m}^2$

4. $7\pi c{m}^2$

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).

1. 22

2. 44

3. 66

4. 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.

$\left(Take\pi as\frac{22}{7}\right)$

1. $616c{m}^2$

2. $51.33c{m}^2$
3. $42c{m}^2$
4. None of the above

Q.

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

1. Purple –Major segment, Yellow –Minor segment

2. None of these

3. Either A or B

4. 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.

1. $(36\sqrt{3}+\frac{660}{7})c{m}^2$

2. $(32\sqrt{3}+\frac{660}{7})c{m}^2$

3. $(36\sqrt{3}+\frac{550}{7})c{m}^2$

4. $(36\sqrt{3}+\frac{660}{9})c{m}^2$

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.

1. 12.5 $c{m}^2$

2. 7.14 $c{m}^2$

3. 19.64 $c{m}^2$

4. 8.8 $c{m}^2$

Q.

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

1. $25\sqrt{3}-\frac{50\pi }{3}c{m}^2$

2. $\frac{50\pi }{3}+25\sqrt{3}c{m}^2$

3. $\frac{50\pi }{3}-25\sqrt{3}c{m}^2$

4. None of these

Q.

Find the area of the shaded region (in $c{m}^2$) as shown in figure of the two concentric circles with centre O and radius 7 $cm$ and 14 $cm$ respectively. Given $\angle$AOC = ${40}^{\circ }$.
(use $\pi$ = $\frac{22}{7}$)

1. 42.1 $c{m}^2$

2. 51.32 $c{m}^2$

3. 67.8 $c{m}^2$

4. 96.5 $c{m}^2$

Q. Tick the correct answer in the following:
Area of a sector of angle p (in degrees) of a circle with radius R is

1. 
2. 
3. 
4. 

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 $m^2$).

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Q. Simplify : $3\sqrt{48}-\frac{5}{2}\sqrt{\frac{1}{3}}+4\sqrt{3}$