Tag: area between two concentric circles

Questions Related to area between two concentric circles

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

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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

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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. $420 : m$

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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. $35$ $cm$

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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
$=\pi (r+h)^2-\pi r^2$
$=\pi(r^2+h^2+2hr-r^2)$
$=\pi(h^2+2hr)$
$=\pi(h+2r)h$

The ratio of the outer and inner circumferences of a circular path is $23:22$, If the path is $5\ m$ wide, the radius of the inner circle is: 

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

  1. $55\ m$

  2. $110\ m$

  3. $220\ m$

  4. $230\ m$

Show answer
Correct Option: B
Explanation:

Given: $r _1=5+r _2$
$\displaystyle \frac {2\pi r _1}{2\pi r _2}=\frac {23}{22}$

$\displaystyle \Rightarrow \frac {r _1}{r _2}=\frac {23}{22}$

$\displaystyle \Rightarrow \frac {5+r _2}{r _2}=\frac {23}{22}$

$\displaystyle \Rightarrow 110+22r _2=23r _2$

$\displaystyle \Rightarrow r _2=110\ m$
$\therefore $ Radius of inner circle$=110\ m$

A circular park has a path of uniform width around it. The difference between the outer and inner circumferences of the circular park is $132$ m. Its width is

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

  1. $20$ m

  2. $21$ m

  3. $22$ m

  4. $24$ m

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Correct Option: B
Explanation:
Let $r _1$ and $C _1$ be the radius and the circumference of the outer circle.
Let $r _2$ and $C _2$ be the radius and the circumference of the inner circle.
The width of the circular path is $(r _1-r _2)$ m.
Given, $C _1-C _2=132$ m
$\Rightarrow 2\pi r _1 - 2\pi r _2=132$
$\Rightarrow 2\pi (r _1-r _2)=132$
$\Rightarrow r _1-r _2=\cfrac{66}{\dfrac{22}{7}}$
$\Rightarrow r _1-r _2=21$
Thus, width of the circular path is $21$ m.

The radius of a circle is increased by 1 cm. Then the ratio of new circumference to the new diameter is

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

  1. $\pi :3$

  2. $\pi :2$

  3. $\pi :1$

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

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Correct Option: C
Explanation:

$New\ radius=r+1\ cm\\ Ratio=2\pi (r+1):2(r+1)=\pi :1$'