Length of an Arc

Q.

If a circle is divided into three equal arcs, each is a major arc. Write True or False. Give a reason for your answer

1. True
2. False

Q.

Segment of a circle is the region between an arc and ………..of the circle.

1. Perpendicular

2. Secant

3. Chord

4. Radius

Q.

State true or false.
If the diameter of a semi-circular protractor is 14 cm then the perimeter will be 36 cm(Approx.)

1. 35

2. 36

Q. When a chord divides the circumference of a circle into two equal arcs, each is called a ___.

1. minor arc
2. major arc
3. semi-circle
4. None of the above

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.

The given figure is a sector of a circle of radius 20 cm. Find the perimeter of the sector.
(Take $\pi$ = 3.14)

1. 55.25 cm

2. 60.93 cm

3. 65.48 cm

4. 70.17

Q.

An arc is _________ .

1. a portion of the segment of a circle

2. a portion of the radius of a circle

3. a portion of the sector of a circle

4. a portion of the circumference of a circle

Q.

The area in $c{m}^2$ of a quadrant of a circle whose circumference is 22 cm is _______

1. 155

2. 15

3. 9.6

4. 16

Q.

The given figure is a sector of a circle of radius 20 cm. Is the perimeter of the sector 61 cm? (Take $\pi =\frac{22}{7}$)

1. True

2. False

Q.

There is a circular swimming pool. There is a bob at the centre of the pool at a distance of $\frac{50}{\pi }$ m from the pool’s wall. Shyam is standing next to the

wall and holding a thread whose other end is connected to the heavy stationary bob at the centre. Holding the thread Shyam now moves along the wall for 20

seconds and the angle between the initial and final positions of the thread is ${12}^{\circ }$. What is Shyam’s speed in metres/minute?

1. 1

2. 5

3. 10

4. 20

Q. Manu has decided to create a triangular flower bed border. He plans to use 3 pieces of rectangular wooden plates with lengths $4,5$ and $6$ feet, as shown in the figure.
Manu plans to cut the 3 pieces of plate for the flower bed border from a single piece of plate. If $\frac{1}{8}$ inch wood is wasted in every cut, calculate the shortest single piece of plate which can be used by Manu.

1. $179$
2. $178$
3. $180$
4. $181$
5. $182$

Q. If radius is 7 cm and angle made at centre of a circle is 180°, then length of the arc is:

1. 56 cm
2. 22 cm
3. 44 cm
4. 32 cm

Q.

O is a fixed point and P is a point which is at a fixed distance from O. If P moves such that angle between initial and final positions of OP is A $<$ ${360}^{\circ }$ then the path taken by P is called __.

Q.

The perimeter of a sector of circle with radius 5.7 m is 27.2 m. The length of the arc of sector (in m) is _______.

1. 15.8

2. 13.4

3. 14.1

4. 16.9

Q.

1. x = (y × θ)/360

2. x = (y × θ)/180

3. y = (x × θ)/360

4. y = (x × θ)/260

Q. Equal chords subtends equal angle at the centre.

1. True
2. False

Q.

1. $28$ cm
2. $14$ cm
3. $7$ cm
4. $10$ cm

Q.

A pendulum swings through an angle of ${30}^{\circ }$ and describes an arc 8.8 cm in length. Find the length of pendulum in cm.

1. 14.5

2. 15.1

3. 17.3

4. 16.8

Q. Find the area of the shaded region in Fig., if $AC=24cm,BC=10cm$ and O is the centre of the circle. (Use $\pi$ $=3.14$).

Q. Equal chords subtends equal angle at the centre.

1. True
2. False

Q. The logarithm form of $3^{-2}=\frac{1}{9}$ is ${\log }_3\frac{1}{9}=m$, then value of $m$ is equal to

1. $-2$
2. $-5$
3. $-3$
4. $-4$

Q.

There is a circular track with the distance of track from centre as 10 m. Ram runs a distance of 21 m on the track. What is the angle in degrees covered by Ram with respect to the centre of track?

1. ${76}^{\circ }$

2. ${63}^{\circ }$

3. ${56}^{\circ }$

4. ${90}^{\circ }$