Tag: circle measures

Questions Related to circle measures

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. $2.62$

Show answer
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 $=\cfrac{7\pi}{6}\times \cfrac{180}{\pi}= 210^{\circ}$

Angle in a semicircle is 

maths circle measures area between two concentric circles the area of ring semicircle and ring

  1. Acute angle

  2. Straight angle

  3. Right angle

  4. Obtuse angle

Show answer
Correct Option: C
Explanation:

Thew intercepted arc for an angle inscribed in a semi-circle is ${180^0}.$ Therefore the measure of the angle must be half of ${180^0}$  or ${90^0}.$

In other word the angle is a right angle$.$
hence,
option $(C)$ is correct answer.

The perimeter of a semi-circular protector is 72 cm then its radius is ____cm.

maths circle measures area between two concentric circles the area of ring semicircle and ring

  1. 36

  2. 28

  3. 14

  4. 7

Show answer
Correct Option: C
Explanation:

Perimeter of Protractor =$ \pi r +2r$


$\rightarrow 72=r(\pi+2)$


$\rightarrow 72=r\dfrac{36}{7}$

$\rightarrow 72 \times \dfrac{7}{36}=r$

$\rightarrow 14\ cm=r$

$Option \ C \ is \ correct$

The radius of a circle is $5: m$. Find the circumference of the circle whose area is $49$ times the area of the given circle.

maths circle measures area between two concentric circles the area of ring semicircle and ring

  1. $220 : m$

  2. $120 : m$

  3. $320 : m$

  4. $420 : m$

Show answer
Correct Option: A
Explanation:
Radius of given circle $=5\ cm$
Therefore,
Area of given circle $=\pi (5)^2$
                              $=25\pi\ cm^2$
Let radius of required circle $ =r$
Therefore,
$\pi r^2=49\times 25\pi$
$\Rightarrow r^2=(7\times 5)^2$
$\Rightarrow r=35$
Therefore,
Circumference $=2\pi r$
                       $=2\times \frac { 22 }{ 7 }\times35$
                       $=220\ m$

Find the area of a ring whose outer and inner radii are $19\ cm$ and $16\ cm$ respectively.

maths circle measures area between two concentric circles the area of ring semicircle and ring

  1. $330\ cm^2$

  2. $310\ cm^2$

  3. $320\ cm^2$

  4. $350\ cm^2$

Show answer
Correct Option: A
Explanation:

Area of outer circle $=\pi{(19)}^2$
                                 $=\cfrac{22}{7}\times 361$
Area of inner circle $=\pi{(16)}^2$
                                 $=\cfrac{22}{7}\times 256$
$\therefore$ area of the ring $=\dfrac{22}{7}\times 361-\dfrac{22}{7}\times 256$
                              $=\cfrac{22}{7}(361-256)$
                              $=\cfrac{22}{7}(105)$
                              $=330\ cm^2$

The area enclosed between two concentric circle is $770$ $cm^2$. If the radius of the outer circle is $21$ $cm$, calculate the radius of the inner circle.

maths circle measures area between two concentric circles the area of ring semicircle and ring

  1. $7$ $cm$

  2. $14$ $cm$

  3. $2.1$ $cm$

  4. $35$ $cm$

Show answer
Correct Option: B
Explanation:

Let radius of the inner circle be $r$ and radius of the outer circle be $R=21cm$


Area enclosed between the two concentric circles $=\pi(R^2-r^2)=770cm^2$

$\Rightarrow 770=\pi(R^2-r^2)$

$\Rightarrow 770=\dfrac{22}{7}(21^2-r^2)$

$\Rightarrow \dfrac{770\times 7}{22}=441-r^2$

$\Rightarrow 245=441-r^2$

$\Rightarrow r^2=196$

$\Rightarrow r=\sqrt{196}$

$\Rightarrow r=14$

Thus, radius of the inner circle $=14$ $cm$

If the radii of two concentric circles are $15 cm$ and $13 cm$, respectively, then the area of the circulating ring in sq cm will be:

maths circle measures area between two concentric circles the area of ring semicircle and ring

  1. $176$

  2. $178$

  3. $180$

  4. $200$

Show answer
Correct Option: A
Explanation:
$R = 15 cm, r = 13 cm. $
Area of the circulating ring $= \pi (R + r)(R - r)$
$= \cfrac {22}{7} (15 + 13) \times (15 - 13)$
$= \cfrac {22}{7} \times 28 \times 2$
$=176$ sq cm

The area of a circular ring between two concentric circles of radii r and (r + h) units respectively is given by

maths circle measures area between two concentric circles the area of ring semicircle and ring

  1. $\pi (2r+h)h\ sq. units$

  2. $\pi (r+h)h\ sq. units$

  3. $\pi (r+2h)h\ sq. units$

  4. $\pi (r-h)h\ sq. units$

Show answer
Correct Option: A
Explanation:
$A = $ area of bigger circle - area of smaller circle
$=\pi (r+h)^2-\pi r^2$
$=\pi(r^2+h^2+2hr-r^2)$
$=\pi(h^2+2hr)$
$=\pi(h+2r)h$