Tag: semicircle and ring

Questions Related to semicircle and ring

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. $269 cm^2$.

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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. $750\pi cm^2$

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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}

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Correct Option: A

measure of angle inscribed in a semicircle is 

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

  1. ${90}^{0} $

  2. ${120}^{0} $

  3. ${100}^{0} $

  4. ${60}^{0} $

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Correct Option: A
Explanation:
The intercepted arc for an angle inscribed in a semi-circle is $180^{\circ}$. 

Therefore the measure of the angle should be half of $180^{\circ}$, or $90^{\circ}$. 

The angle is a right angle.

Points $P,Q,R$ lie on same line. Three semi circles with the diameters $PQ,QR,PR$ are drawn on same side of line segment $PR$. The centres of the semicircles are $A,B,O$ respectively. A circle with centre $C$ touches all $3$ semi circles then the radius of this circle is $\left(AQ=a,BQ=b\right)$

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

  1. $\dfrac{ab}{a+b}$

  2. $\dfrac{ab\left(a+b\right)}{a^{2}+b^{2}}$

  3. $\dfrac{ab\left(a+b\right)}{a^{2}+ab+b^{2}}$

  4. $\dfrac{ab\left(a+b\right)}{\left(a-b\right)^{2}}$

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Correct Option: A

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. $\Delta /s$

  3. $\frac { 2\Delta }{ a+b } $

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

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Correct Option: A