Tag: length of an arc

Questions Related to length of an arc

What is the length of an arc of a circle with a radius of $5$ if it subtends an angle of ${60}^{o}$ at the center?

maths circle measures length of an arc area of a sector of a circle sector and arc of a circle

  1. $3.14$

  2. $5.24$

  3. $10.48$

  4. $2.62$

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Correct Option: B
Explanation:
Given:
Radius (r)$=5$
Angle $=60^o$

Arc length for a particular angle we can write as -
$=\dfrac{\theta}{360}\times (2\pi r)$

$=\dfrac{60}{360}\times 2\pi \times 5$

$=\dfrac{10\pi}{6}=5.24$

Option 'B'.

If the sector of a circle of diameter $10$ cm subtends an angle of $144^{\circ}$ at the centre, then the length of the arc of the sector is

maths circle measures length of an arc area of a sector of a circle sector and arc of a circle

  1. $2\pi $ cm

  2. $4\pi $ cm

  3. $5\pi$ cm

  4. $6\pi $ cm

Show answer
Correct Option: B
Explanation:
Given, diameter $=10$ cm, $\theta=144^o$
Length of an arc of a circle $=\dfrac { \theta  }{ 360 } \times 2\pi { r }=\dfrac { 144 }{ 360 } \times 2\pi \times \dfrac { 10 }{ 2 } =4\pi $ cm 
Hence, option B is correct.

A circular wire of radius $7$ cm is cut and bend again into an arc of a circle of radius $12$ cm. The angle subtended by the arc at the centre is

maths circle measures length of an arc area of a sector of a circle sector and arc of a circle

  1. $50^\circ$

  2. $210^\circ$

  3. $100^\circ$

  4. $60^\circ$

Show answer
Correct Option: B
Explanation:

Given, radius of circular wire $= 7$ cm

Circumference of wire $= 2 \pi r = 2 \pi (7) = 14 \pi$
Radius of arc $= 12$ cm

Angle subtended by the arc $= \dfrac{\text{arc}}{\text{radius}} = \dfrac{14 \pi}{12} = \dfrac{7 \pi}{6}$

Angle subtended by arc $=\cfrac{7\pi}{6}\times \cfrac{180}{\pi}= 210^{\circ}$