Tag: arcs and sectors

Quizzes (0) Questions (23)

Questions Related to arcs and sectors

Multiple choice maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

$r$ is the radius and $l$  is the length of an arc. The area of a sector is ______.

  1. $\dfrac { 1 } { 2 } r l$
  2. $\dfrac { 3 } { 2 } r ^ { 2 } l$
  3. $\dfrac { 4 } { 3 } r l$
  4. $\dfrac { 3 } { 2 } r l$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\begin{array}{l} Area\, of\, a\, \sec  tor\, =\dfrac { 1 }{ 2 } { r^{ 2 } }\theta  \ =\dfrac { 1 }{ 2 } \times r\times r\theta  \ =\dfrac { 1 }{ 2 } \times r\times l \ Hence,\, option\, A\, is\, \, the\, \, correct\, \, answer. \end{array}$

Multiple choice maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

A circular disc of radius $10 cm$ is divided into sectors with angles $120^o$ and $150^o$, then the ratio of the area of two sectors is

  1. $4 : 5$
  2. $5 : 4$
  3. $2 : 1$
  4. $8 : 7$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of sector formed from angle $\theta=\dfrac{\theta}{360^\circ}\pi r^2$, where $r$ is the radius of the circle
Now, if angle is $120^\circ$, $150^\circ$ then the ratio of area of sector will be

$\Rightarrow\dfrac{\dfrac{120^\circ}{360^\circ}\pi r^2}{\dfrac{150^\circ}{360^\circ}\pi r^2}$

$\Rightarrow \dfrac{4}{5}$
Hence, the required ratio is $4:5$. 

Multiple choice maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

The region between an arc and two radii joining the centre to the end points of the arc is called

  1. sector

  2. segment

  3. semicircle

  4. non of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The region between an arc and two radii joining the center to the end points of the arc is called sector.The minor are corresponds to minor sector  and  major arc correspond to major sector.

Multiple choice maths circle and its elements angle subtended by arc sector of a circle arcs and sectors
$\triangle ABC$ is inscribed in a circle. Point $P$ lies between $A$ and $C$, whereas point $Q$ lies between $B$ and $C$. If $m(\text{arc}\, APC) = 60^\circ$ and $\angle BAC = 80^\circ$, find $m(\text{arc}\, BQC)$.
  1. $180^\circ$
  2. $90^\circ$
  3. $160^\circ$
  4. $120^\circ$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

By inscribed angle theorem, 

$ \cfrac 12 m\angle BAC = m(arc BQC)$
$m(arc BQC) = 2 \times \angle BAC$
$\therefore m(arc BQC) = 2 \times 80^o = 160^o$