Tag: circle measures

Quizzes (4) Questions (131)

Questions Related to circle measures

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

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: 

  1. $55\ m$
  2. $110\ m$
  3. $220\ m$
  4. $230\ m$
Reveal answer Fill a bubble to check yourself
B Correct answer
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$=110\ m$

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

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

  1. $20$ m
  2. $21$ m
  3. $22$ m
  4. $24$ m
Reveal answer Fill a bubble to check yourself
B Correct answer
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.
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.