Tag: the area of ring

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Questions Related to the area of ring

Multiple choice maths circle measures area between two concentric circles the area of ring 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

  1. 500

  2. 600

  3. 700

  4. 800
Reveal answer Fill a bubble to check yourself
A Correct answer
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=$\frac{1540\times 100}{308}=\frac{154000}{308}=500$

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

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

  1. $255 cm^2$.
  2. $148 cm^2$.
  3. $324 cm^2$.
  4. $269 cm^2$.
Reveal answer Fill a bubble to check yourself
D Correct answer
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 } $

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

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.

  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. $\frac{{\sqrt 3 }}{4} + \frac{\pi }{{24}}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The lune area is calculated by finding the area of the smaller semicircle and subtracting the overlapping segment area. The geometry involves a 60-degree sector or similar trigonometric relations.

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

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 $\left(AQ=a,BQ=b\right)$

  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. $\dfrac{ab\left(a+b\right)}{\left(a-b\right)^{2}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a classic geometry problem involving the Sangaku theorem or properties of circles tangent to a line. The radius of the circle tangent to three semicircles with diameters a, b, and a+b is given by r = (a * b) / (a + b).