Length of Arc of a Sector

Q.

In the given figure, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.

Q. Question 16
A piece of wire 20 cm long is bent into the form of an arc of a circle subtending an angle of ${60}^{\circ }$ at its centre. Find the radius of the circle.

Q.

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

Q. Angle subtended by any chord of a circle at the centre of a circle is ___ the angle subtended at the major arc by the same chord.

Q.

Area of a sector of a circle of radius 36 cm is 54π cm². The length of the corresponding arc of the sector is:

1. 2 π cm

2. 4 π cm

3. 3 π cm

4. 5 π cm

Q.

The length of an arc of a sector of angle ${\theta }^{\circ }$ of a circle with radius R is

(a) $\frac{2\pi R\theta }{180}$

(b) $\frac{2\pi R\theta }{360}$

(c) $\frac{\pi R^2\theta }{180}$

(d) $\frac{\pi R^2\theta }{360}$

Q.

The length of an arc of a circle, subtending an angle of ${54}^{\circ }$ at the centre is 16.5 cm. Calculate the radius, circumference and area of the circle.

Q. A path of 4 m width runs round a semi-circular grassy plot whose circumference is 163 $\frac{3}{7}$ m Find:

(i) the area of the path

(ii) the cost of gravelling the path at the rate of Rs 1.50 per square metre

(iii) the cost of turfing the plot at the rate of 45 paise per m².

Q.

Q. The cost of fencing a circular field at the rate of Rs 25 per metre is Rs 5500. The field is to be ploughed at the rate of 50 paise per m² . Find the cost of ploughing the field. [Take $\mathrm{\pi }=\frac{22}{7}$].

Q.

In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and $\angle AOB={90}^{\circ }$. If AO = OB = 42 cm then find the perimeter of the top of the table.

Q.

Find the angle subtended at the centre of a circle of radius 'a' by an arc of length $\left(\frac{a\pi }{4}\right)cm$

Q.

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in figure. Find.

(i) The total length of the silver wire required.

(ii) The area of each sector of the brooch

Q. In the given figure, three sectors of a circle of radius 7 cm, making angles of 60°, 80° and 40° at the centre are shaded. Find the area of the shaded region. [CBSE 2012]

Q.

The given figure is a sector of a circle of radius 20 cm. Find the perimeter of the sector. $Take\pi =\frac{22}{7}$

1. 55

2. 61

3. 65

4. 70

Q.

Which of the following statement is true for the longest chord of a circle?

1. It is equal to radius.

2. It is two times of radius.

3. It is never equal to the diameter.

4. It is two times of diameter.

Q.

An arc of length $20\pi cm$ subtends an angle of ${144}^{\circ }$ at the centre of a circle. Find the radius of the circle.

Q. If the circumference of a circle is equal to the perimeter of a square then the ratio their areas is:

(a) 22 : 7

(b) 14 :11

(c) 7 :22

(d) 7 :11

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

Q.

Q. A wire is bent to form a circle of radius 7 cm. From the resulting shape, a chunk of the wire is cut off, and the wire cut off measures 4 cm in length. The length of the remaining wire is

1. 45 cm
2. 50 cm
3. 42 cm
4. 40 cm

Q.

From a circular piece of cardboard of radius 3 cm, two sectors of ${90}^{\circ }$ have been cut off. Find the perimeter of the remaining portion nearest hundredth centimeters. (Take $\pi =\frac{22}{7}$)

Q.

A circle with centre O, diameter AB and a chord AD is drawn. Another circle is drawn with AO as diameter to cut AD at C, then BD = 2 OC.

1. BD =3 OC

2. BD = 2 OC

3. BD = OC

4. 2BD = OC

Q.

An arc of length 15 cm subtends an angle of ${45}^{\circ }$ at the centre of a circle. Find in terms of $\pi$, the radius of the circle.

Q. A sector is cut-off from a circle of radius 21 cm. The angle of the sector is 120°. Find the length of its arc and the area.

Q.

In a circle of radius 35 cm, an arc subtends an angle of ${72}^{\circ }$ at the centre. Find the length of the arc and area of the sector.

Q.

Find, in terms of the $\pi$, the length of the arc that subtends an angle of ${30}^{\circ }$ at the centre of a circle of radius 4 cm.

Q. A square made from a wire of length 44 cm is restructured to form a circle. Find the area of the circle formed.

1. 154 $c{m}^2$
2. 44 $c{m}^2$
3. 84 $c{m}^2$
4. 200 $c{m}^2$

Q.

Derive the formula used to find the area of sector and length of arc of sector. [2 MARKS]

Q. ___ is the sector of a circle in which major arc is the part of its boundary.

1. Major sector
2. Minor sector
3. Minor Segment
4. Major segment