Area of a Sector

Q. Area of a sector of circle of radius 12 cm and subtending an angle of 60${}^{\circ }$ at the centre is $c{m}^2$.

1. $12\pi$
2. $24\pi$
3. $240\pi$
4. $60\pi$

Q. Question 4
Find the area of the shaded region in Fig. 12.22, 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.

Q. Question 15
In figure arcs have been drawn of radius 21 cm each with vertices A, B, C and D of quadrilateral ABCD as centres. Find the area of the shaded region.

Q.

Question 6
In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in Fig. 12.24. Find the area of the design.

Q. Find the area of the major sector of a circle with radius 42 cm and of angle 30°.
(Use π = $\frac{22}{7}$

1. 5082

Q. Question 5 (ii)
In a circle of radius 21 cm, an arc subtends an angle of ${60}^{\circ }$ at the centre. Find:
(ii) area of the sector formed by the arc

Q. Question 14
Tick the correct answer in the following:
Area of a sector of angle p (in degrees) of a circle with radius R is
(A) $\frac{p}{180}\times 2\pi R$
(B) $\frac{p}{180}\times \pi R^2$
(C) $\frac{p}{360}\times 2\pi R$
(D) $\frac{p}{720}\times 2\pi R^2$

Q.

The area of a sector (in $c{m}^2$ )of a circle with radius 6 cm if angle of the sector is ${70}^{\circ }$ will be __ $c{m}^2$. ( Take $\pi$ = $\frac{22}{7}$)

Q. Question 3
Find the area of a sector of a circle of radius 28 cm and central angle ${45}^{\circ }$.

Q. Question 1
Find the area of a sector of a circle with radius 6 cm if angle of the sector is ${60}^{\circ }$.

Q. Find the area of a sector of a circle with radius 6cm if the angle of the sector is ${60}^{\circ }$

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. Question 4
A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector. $(Use\pi =3.14)$

Q. Find the area of the major sector of a circle with radius 42 cm and of angle 30°.
(Use π = $\frac{22}{7}$

1. 5082

Q. Find the area of a sector of a circle with radius $6cm$ if angle of the sector is ${60}^{\circ }.$

Q. What is the area of a quadrant of a circle whose circumference is 22 cm?
$(\pi =\frac{22}{7})$

1. $\frac{77}{8}c{m}^2$
   
2. $\frac{49}{16}c{m}^2$
   
3. $\frac{77}{16}c{m}^2$
   
4. $\frac{49}{8}c{m}^2$
   

Q.

The radius of a circle is 7 cm and it forms a sector by rotating through 60${}^{\circ }$. Then, the radius gets doubled and further moves 30${}^{\circ }$ to form another sector. What is the area of the total region covered by the radius? ( Take π= $\frac{22}{7}$)

1. 308 $c{m}^2$

2. 154 $c{m}^2$

3. 77 $c{m}^2$

4. 144 $c{m}^2$

Q. Question 8
Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.

Q.

A chord of a circle of radius 12 cm subtends an angle of ${120}^{\circ }$ at the centre. Find the area in $c{m}^2$ of the corresponding segment of the circle. (Use $\pi$ = 3.14 and $\sqrt{3}$ = 1.73)

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Q.

The area in $c{m}^2$ of a sector of a circle with radius 6 cm and angle of the sector ${60}^{\circ }$ is 20.

1. True

2. False

Q. In a circle of radius 21 cm, an arc subtends an angle of ${60}^{\circ }$ at the centre the length of the arc is 22 cm.

1. False
2. True
3. Neither
4. Either

Q. Question 20
Find the difference of the areas of a sector of angle ${120}^{\circ }$ and its corresponding major sector of a circle of radius 21 cm.

Q. An isosceles triangle has its base of $20$ cm and each of its equal sides is $26$ cm long. Calculate its area

1. $250$
2. $240$
3. $156$
4. none of the above

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

Q. The radius of a certain circle is $30$ cm find the approximate length of an arc of this circle; if the length of the chord of the arc be $30$ cm

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.

A circle of diameter 6 cm makes a sector of angle $P^{\circ }$, what will be the area of the sector?

1. (P/ 720⁰) ×π × 3²

2. (P/ 360⁰) ×π × 3²

3. (P/ 360⁰) ×π × 6²

4. (P/ 180⁰) ×π × 3²

Q. Choose the major sector in the given figure.

1. 
2. 
3.