Tag: length of an arc

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Questions Related to length of an arc

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

A sector of a circle with sectorial angle of $\displaystyle 36^{\circ} $ has an area of 15.4 sq cm The length of the arc of the sector is

  1. $8.8 m$
  2. $4.4 m$
  3. $0.22 m$
  4. $0.44 m$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\displaystyle \frac{36}{360}\times \frac{22}{7}r^{2}=15.4\Rightarrow r^{2} =\frac{15.4\times 5\times 7}{11}=49$
$\displaystyle \Rightarrow r=7$
$\displaystyle C=2\pi r=2\times \frac{22}{7}\times 7=44cm$
$\displaystyle =0.44 m$

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

In a circle of radius 21 cm an arc subtends an angle of $\displaystyle 56^{\circ} $ at the centre of the circle. The length of the arc is

  1. $20.53$ cm
  2. $17.53$ cm
  3. $15.53$ cm
  4. $16.53$ cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\displaystyle \theta =56^{\circ},r=21cm$
Length. of $\displaystyle AB=\dfrac{56^{\circ}}{360^{\circ}}\times 2\times \dfrac{22}{7}\times 21$
$\displaystyle =\dfrac{616}{30}=20.53cm$

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

What is the length of arc AB making angle of $126^0$ at center of radius $8$?

  1. $2.6\displaystyle \pi $
  2. $5.6\displaystyle \pi $
  3. $7.6\displaystyle \pi $
  4. $\displaystyle \frac{1}{2}\pi $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Setting a proportion 
AB : OB : : 126 : 360
$\displaystyle \frac{\overline{AB}}{2\pi r}=\frac{126}{360}$
$\displaystyle \overline{AB}=\left ( \frac{126}{360} \right )\times 2\pi r$
$\displaystyle \overline{AB}=\left ( \frac{126}{360} \right )\times 2\pi \times 8$
$\displaystyle \overline{AB}=5.6\pi $

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

If an arc of a circle of radius 14 cm subtends an angle of $60^{\circ}$ at the centre, then the length of the arc is $\displaystyle \frac{44}{3} cm$.

  1. True

  2. False

  3. Niether

  4. Either
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Arc length = (theta / 360) * 2 * pi * r. Here, (60 / 360) * 2 * (22 / 7) * 14 = (1 / 6) * 2 * 22 * 2 = 88 / 6 = 44 / 3 cm. The statement is true.

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

The length of an arc of a sector of a circle of radius r units and of centre angle $\theta$ is $\displaystyle \frac{\theta}{360^{\circ}} \times \pi r^2$.

  1. True

  2. False

  3. Neither

  4. Either
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The formula provided, (theta / 360) * pi * r^2, is the formula for the area of a sector, not the length of an arc. The arc length formula is (theta / 360) * 2 * pi * r.

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

Length of an arc of a circle with radius $r$ and central angle $\theta$ is(angle in radians):

  1. $\dfrac{r\times \theta}{360^{o}}$
  2. $\dfrac{r\times \theta}{180^{o}}$
  3. $\dfrac{r\times \theta}{90^{o}}$
  4. $r\times \theta$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Let $r$ be the radius of a circle and $\theta$ be the central angle
Length of an arc of the sector $=r\times \theta$
Hence, length of an arc of a circle $=r\times \theta$.
Multiple choice maths circle measures length of an arc area of a sector of a circle sector and arc of a circle
The diameter of a circle is $10$ cm, then find the length of the arc, when the corresponding central angle is $180^{\circ}$.  $(\pi =3.14)$
  1. $15.7$
  2. $16$
  3. $3.14$
  4. $18$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Radius of the circle $ = \dfrac {\text{Diameter}}{2} = 5 $ cm 


Length of an arc subtending an angle $ \theta  = \dfrac { \theta  }{ 360 }

\times 2\pi R $, where $R$ is the radius of the circle. 

So, length of the arc $ = \dfrac {180}{360} \times 2 \times 3.14\times 5  = 15.7 $ cm