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

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).

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

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

  1. 550 $cm^{2}$
  2. 425 $cm^{2}$
  3. 496 $cm^{2}$
  4. 810 $cm^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a ring shaped region$=\pi(20)^2-\pi(15)^2$
                                                    $=(400-225)\times \dfrac{22}{7}$
                                                    $=(175)\times \dfrac{22}{7}$
                                                   $ =550$ sq. cm

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 outer and inner circumference of the circular path is $132\ m$. Its width is _____ $\displaystyle \left(\pi=\frac{22}{7}\right)$

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

Given $\displaystyle 2\pi r _{2}-2\pi r _{1}=132$
$\displaystyle \Rightarrow r _{2}-r _{1}=\frac{132}{2\pi }=\frac{132\times 7}{44}=21\ m$

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

The inner circumference of a circular track $14\ m$ wide is $440\ m$. The radius of the outer circle is

  1. $70\ m$
  2. $56\ m$
  3. $77\ m$
  4. $84\ m$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Inner circumference $= \displaystyle 2\pi r=2\times \frac{22}{7}\times r=\frac{44r}{7}$
Given $\displaystyle \frac{44r}{7}=440\Rightarrow r=\frac{440\times 7}{44}=70\ m$
$\displaystyle \therefore $ Radius of outer circle $= 70\ m + 14\ m = 84\ m$ 

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

If the perimeter of a semi-circle is $36\ cm$. What will be its diameter?

  1. $88\ cm$
  2. $22\ cm$
  3. $28\ cm$
  4. $14\ cm$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Perimeter of semicircle$=36cm$
$\pi r+d=36$
$\Rightarrow \pi r+2r=36$
$\Rightarrow r\left( \cfrac { 22 }{ 7 } +2 \right) =36$
$\Rightarrow \cfrac { 36 }{ 7 } \times r=36$
$\Rightarrow r=7$
$\therefore $ Diameter $2r=2\times 7=14cm$
Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

If a wire is bent into the shape of a square the area of the square is 81 sq cm .When the wire is bent into a semi circular shape; what is the area of the semicircle? $\displaystyle \left ( \pi =\frac{22}{7} \right )$

  1. $\displaystyle 77\:\text{cm}^{2}$
  2. $\displaystyle 73\:\text{cm}^{2}$
  3. $\displaystyle 37\:\text{cm}^{2}$
  4. $\displaystyle 33\ \text{cm}^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let '$a$' be the length of each side of the square
Then $\displaystyle a^{2}=81\Rightarrow a=9$ cm
Length of wire $=$ Perimeter of square
=$ 4a= 36$ cm
$\displaystyle \Rightarrow $ Circuference of semicircle $= 36$ cm
$\displaystyle \Rightarrow \pi r+2r=36$

$ \displaystyle \Rightarrow r\left ( \pi +2 \right )=36$
$\displaystyle \Rightarrow  r =\dfrac{36}{\pi +2}=\dfrac{36}{\dfrac{22}{7}+2}=\dfrac{36\times 7}{\left ( 22+14 \right )}=\dfrac{36\times 7}{36}$ cm $=7$ cm
$\displaystyle \therefore \ \text{Area of the semicircle}=\frac{1}{2}\pi r^{2}$
$\displaystyle =\dfrac{1}{2}\times \dfrac{22}{7}\times 7\times \text{cm}^{2}=77\text{cm}^{2}$

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

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

  1. $176$
  2. $178$
  3. $180$
  4. $200$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$R = 15\ cm, r = 13\ cm$
Area of the circulating ring 
$\displaystyle = \pi \left(R^2-r^2\right)$

$\displaystyle =\pi \left ( R+r \right )\left ( R-r \right )$
$\displaystyle =\frac{22}{7}\left ( 15+13 \right )\times \left ( 15-13 \right )$
$\displaystyle \frac{22}{7}\times 28\times2$
$= 176$ sq cm