Tag: maths

Questions Related to maths

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

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

  1. $2.6\displaystyle \pi $

  2. $5.6\displaystyle \pi $

  3. $7.6\displaystyle \pi $

  4. $\displaystyle \frac{1}{2}\pi $

Show answer
Correct Option: B
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 $

If the radius and arc length of a sector are 17 cm and 27 cm respectively, then the perimeter is

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

  1. 16 cm

  2. 61 cm

  3. 32 cm

  4. 80 cm

Show answer
Correct Option: B
Explanation:

Perimeter of the Sector = 2(Radius of the circle) + Arc Length 


$Perimeter = 2(17) + 27 = 2*17 +27 = 61cm$

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 $\displaystyle \frac{44}{3} cm$.

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

  1. True

  2. False

  3. Niether

  4. Either

Show answer
Correct Option: A

In a circle of radius 21 cm, an arc subtends an angle of $60^{\circ}$ at the centre the length of the arc is 22 cm.

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

  1. True

  2. False

  3. Neither

  4. Either

Show answer
Correct Option: A

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

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

  1. True

  2. False

  3. Neither

  4. Either

Show answer
Correct Option: B

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

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

  1. $\dfrac{r\times \theta}{360^{o}}$

  2. $\dfrac{r\times \theta}{180^{o}}$

  3. $\dfrac{r\times \theta}{90^{o}}$

  4. $r\times \theta$

Show answer
Correct Option: D
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 $=r\times \theta$.

If $ABC$ is an are of a circle and $\angle ABC=135^{o}$, then the ratio of arc $ ABC$ to the circumference is:

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

  1. $1 :4$

  2. $3:4$

  3. $3:8$

  4. $1:2$

Show answer
Correct Option: A
The diameter of a circle is $10$ cm, then find the length of the arc, when the corresponding central angle is $180^{\circ}$.  $(\pi =3.14)$
maths circle measures length of an arc area of a sector of a circle sector and arc of a circle

  1. $15.7$

  2. $16$

  3. $3.14$

  4. $18$

Show answer
Correct Option: A
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

The diameter of a circle is $10$ cm, then find the length of the arc, when the corresponding central angle is $144^{\circ}$.$(\pi =3.14)$
maths circle measures length of an arc area of a sector of a circle sector and arc of a circle

  1. $44$ cm

  2. $12.56$ cm

  3. $12$ cm

  4. $88$ cm

Show answer
Correct Option: B
Explanation:

Radius of the circle $ = \dfrac {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 {144}{360} \times 2 \times 3.14 \times 5  = 12.56  cm $

A sector is cut from a circle of radius $21$ cm. The angle of the sector is $150^o$. Find the length of its arc and area.

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

  1. $27$ cm and $412.7cm^2$

  2. $36$ cm and $436.9cm^2$

  3. $45$ cm and $517.5cm^2$

  4. $55$ cm and $577.5cm^2$

Show answer
Correct Option: D
Explanation:

The length of arc $l$ and area $A$ of a sector of angle $\theta$ in a circle of radius $r$ are given by,


$l=\displaystyle\frac{\theta}{360^o}\times 2\pi r$

and $A=\displaystyle\frac{\theta}{360^o}\times \pi r^2$ respectively.

Here, $r=21$ cm and $\theta=150^0$


$\therefore l = \dfrac{150}{360}\times2\times\dfrac{22}7\times21 = 55$ cm

and 

$A = \dfrac{150}{36}\times\dfrac{22}7\times21^2 = \dfrac{1155}2 = 577.5\ {cm}^2$