Length of an Arc

Q. The arc length of a quarter circle with radius $r$ and diameter $d$ can be written as

1. $2\mathrm{\pi r}$
2. $\mathrm{\pi r}$
3. $\frac{\mathrm{\pi d}}{2}$
4. $\frac{\mathrm{\pi r}}{2}$

Q. A circle of radius 120 m is divided into 8 equal sectors. Find the length of the arc of each of the sectors.

1. $20\pi m$
2. $30\pi m$
3. $40\pi m$
4. $50\pi m$

Q.

The perimeter of a circle and its diameter vary _______ with each other.

Q. The arc length of a semi circle and quarter circle describe quarter and half the circumference of a circle with the same radius.

1. True
2. False

Q. If the angle subtened by the radii at the center of a circle of circumference 60 cm is 30 degree, what will be the length (in cm) of the minor arc formed?

Q. Given a semicircle with radius and diameter of $r$ and $d$ respectively, the arc length of a semicircle can be written as

1. $2\mathrm{\pi r}$
2. $\mathrm{\pi d}$
3. $\frac{\mathrm{\pi r}}{2}$
4. $\frac{\mathrm{\pi d}}{2}$

Q. What will be the length of the remaining arc, if three-quaters of a circle of radius 20 cm is removed?
$\text{Take}\pi =3.14$

Q. Given that a circle with radius $r$ has a segment which subtends an angle $\theta <{180}^{\circ }$at the centre, then the length of the arc described by that segment is given by:

1. $\frac{\theta }{{180}^{\circ }}\times \pi d$

2. $\frac{\theta }{{360}^{\circ }}\times \pi d$
3. $\frac{\theta }{{180}^{\circ }}\times 2\pi r$
4. $\frac{\theta }{{360}^{\circ }}\times \pi r$

Q. If skating track of length 55 m, as shown in figure, subtends ${150}^o$ angle at center of circle, find radius of circle.

1. 42 m
2. 11 m
3. 14 m
4. 21 m

Q. If the length of the major arc formed when the radii subtend an angle of $120$ degree at the center is $150cm$, find the circumference of the circle.

1. $450cm$
2. $180cm$
3. $225cm$
4. None of the above

Q. The minor arc formed by two radii subtending an angle of $50$ degree at the center of a circle is $20$ cm in length. Find the radius of the circle.
Take $\pi =3.14$

1. $48.56cm$
2. $22.93cm$
3. $45.86cm$

Q. The radius of a circular wheel is 49 inches. The circumference of the wheel is inches.
$\text{[Take π=}\frac{22}{7}]$

1. 154
2. 308
3. 616