Tag: circle measures

Questions Related to circle measures

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. $230\ m$

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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:

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

The diameter of a wheel is 98 cm The number of revolutions it will have to cover a distance of 1540 m is

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

  1. 500

  2. 600

  3. 700

  4. 800

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Correct Option: A
Explanation:

Given the diameter of wheel is 98 cm

Then radius of wheel =$\frac{98}{2}=49cm$
Then circumference of wheel =$2\times \frac{22}{7}\times 49=308cm$
Then the number of revolution in distance of 1540 m=$\frac{1540\times 100}{308}=\frac{154000}{308}=500$

What is the area of the circular ring included between two concentric circles of radius $14$ cm and $10.5$ cm ? 

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

  1. $255 cm^2$.

  2. $148 cm^2$.

  3. $324 cm^2$.

  4. $269 cm^2$.

Show answer
Correct Option: D
Explanation:

 Area of the circular ring = $\frac { 22 }{ 7 } \times \left( { R }^{ 2 } - { r }^{ 2 } \right)$ = $ \frac { 22 }{ 7 } \times \left( { 14 }^{ 2 } - { 10.5 }^{ 2 } \right)$ = $269.5 \ { cm }^{ 2 }\approx 269\ { cm }^{ 2 } $

If the outer and inner radii of a ring are $10$ cm and $8$ cm, then its area is nearly

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

  1. $113.443$ sq. cm

  2. $113.343$ sq. cm

  3. $113.243$ sq. cm

  4. $113.143$ sq. cm

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Correct Option: D
Explanation:

$Area=\pi (100^{2} - 8^{2}) = \pi 36 = 113.143\ cm^{2}$.

Find the area of a ring shaped region enclosed between two concentric circles of radii $20$ cm and $15$ cm.

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

  1. $175\pi cm^2$

  2. $75\pi cm^2$

  3. $275\pi cm^2$

  4. $750\pi cm^2$

Show answer
Correct Option: A
Explanation:
$x=1$ 
$r _{1}=20cm$ 
$r _{2}=15cm$
 $Area = \pi (r _{2}^{2}-r _{1}^{2})$ 
$^{2}\pi ((20)^{2}-(15)^{2})$ 
$\pi (400-225)$ 
$=775\pi cm^{2}$

A lawn is in the shape of a semi-circle of diameter $35$ $dm$. The lawn is surrounded by a flower- bed of width $3.5\ dm$ all around. Find the area of the flower bed in $d m ^ { 2 }$.

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

  1. $407.8895$

  2. $403.8825$

  3. $407.2343$

  4. $409.2543$

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Correct Option: B

A semicircle of diameter 2 is drawn. Two point on the semicircle are chosen so that they are 1 unit apart. A  semicircle of diameter 1 is the drawn with those two point as the 'endpoints' . The shaded area inside this smaller semicircle and outside the larger semicircle is called a lune. Determine the area of this lune.

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

  1. $\frac{\pi }{6} - \frac{{\sqrt 3 }}{4}$

  2. $\frac{{\sqrt 3 }}{4} - \frac{\pi }{{12}}$

  3. $\frac{{\sqrt 3 }}{4} - \frac{\pi }{{24}}$

  4. $\frac{{\sqrt 3 }}{4} + \frac{\pi }{{24}}$

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Correct Option: B

In a triangle with sides $a$, $b$, and $c$, a semicircle touching the sides $AC$ and $CB$ is inscribed whose diameter lies on $AB$. Then the radius of the semicircle is

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

  1. $a/2$

  2. $\triangle/s$

  3. $\dfrac{2\triangle}{a+b}$

  4. $\dfrac{2\ abc}{(s)(a+b)}\cos\dfrac{A}{2}\cos\dfrac{B}{2}\cos\dfrac{C}{2}

Show answer
Correct Option: A