Mathematics · Quantitative Aptitude

Circle Geometry

250 Questions

Circle geometry focuses on the properties and dimensions of circles, including radius, diameter, circumference, and area calculations. Questions often involve concentric circles, sectors, and inscribed shapes. This topic frequently appears in quantitative aptitude sections of major competitive exams.

Area and circumferenceConcentric circlesCircle sectorsInscribed polygonsSemicircle area

Circle Geometry Questions

Multiple choice maths area of complex plane figures 2d and 3d figures

A square is inscribed in a circle of radius $7: cm$. Find area of the square.

  1. $98 \: cm^{2}$
  2. $97 \: cm^{2}$
  3. $91 \: cm^{2}$
  4. $90 \: cm^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given,
Radius of the circle $=7:cm$
Let the side of the square be $a:cm$.
A square when inscribed in a circle then the diameter of the circle must be diagonal of the square.
Therefore,
Diagonal of square $=\sqrt {a^2+a^2}$
                                 $=a\sqrt 2$
Now,
Diameter of the circle $=2\times 7$
                                  $=14:cm$
$=>\sqrt 2 a=14$
$=>a=\dfrac{14}{\sqrt 2}$
$=>a=7\sqrt 2: cm$
Therefore,
Area of square $=a^2$
                       $=(7\sqrt 2 cm)^2$
                       $=(7\sqrt 2 cm)(7\sqrt 2 cm)$
                       $=98: cm^2$

Multiple choice maths area of complex plane figures 2d and 3d figures

The ratio of areas of square and circle is given n : 1 where n is a natural number. If the ratio of side of square and radius of circle is k :1, where k is a natural number, then n will be multiple of

  1. $77$
  2. $22$
  3. $154$

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let a be the side of the square & r be the radius of the circle, then $\dfrac {a^2}{\pi r^2}=n$
Now, $\dfrac {a}{r}=k$
$k=\dfrac {a}{r}=\sqrt {\dfrac {22\times n}{7}},n$ has to be multiple of $22\times 7=154$.

Multiple choice maths area of complex plane figures 2d and 3d figures

If one side of a square is 2.4 m. Then what will be the area of the circle inscribed in the square?

  1. $1.44 \displaystyle\, m^{2} $
  2. $\displaystyle 1\frac{11}{25}\pi $ $\displaystyle m^{2} $
  3. $\displaystyle \frac{11}{25}\pi $ $\displaystyle m^{2} $

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The radius of the circle inscribed in the square
of side 2.4m
$\displaystyle r=\dfrac{2.4}{4}m=1.2m$
$\displaystyle \therefore$ Area of the circle $\displaystyle =\pi r^{2}$ square units
$\displaystyle =\pi \times 1.2 m\times 1.2 m$
$\displaystyle =1.44 \pi m^{2}$

$\displaystyle =1\dfrac{11}{25}\pi m^{2}$
$\displaystyle \therefore $ The required area $\displaystyle =1\frac{11}{25}\pi m^{2}$

Multiple choice maths area of complex plane figures 2d and 3d figures

Four circular cardboard pieces of radii $7 cm$ are placed on a paper in such a way that each piece touches other two pieces. The area of the  region enclosed between these pieces   is

  1. $42$ $cm^2$
  2. $21$ $cm^2$
  3. $84$ $cm^2$
  4. $96$ $cm^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The diameter of circle =$2\times 7=14$ cm

The circles together formed a shape  square diameter of 2 circle to get from a side =$2\times 14=28$ cm 
Then area of square =$a^{2}=(28)^{2}=784 cm^{2}$
And area of each  circle =$\pi r^{2}=\frac{22}{7}\times (7)^{2}=154 cm^{2}$
So area of four circles =$4\times 154=616 cm^{2}$
Then area of region enclosed between these pieces $= 784-616=168$ sq cm
Then area of region enclosed between one  pieces=$\frac{168}{4}=42 cm^{2}$

Multiple choice maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

The area of a circle inscribed in a regular hexagon is $100\pi$. The area of the hexagon is:

  1. $600$
  2. $300$
  3. $200\sqrt { 2 } $
  4. $200\sqrt { 3 } $
  5. $200\sqrt { 5 } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Area of circle $=100\pi $
$\pi r^{2}=100\pi $
$r^{2}=100$
$r=10$
Now, a regular hexagon is made up of 6 equilateral $\bigtriangleup s $ of equal areas. Now, height of equilateral $\bigtriangleup  $ is equal to radius of circle.Therefore, ar. of 1 equilateral $\bigtriangleup=\dfrac {1}{2} $ x base x height
$\Rightarrow \dfrac {\sqrt{3}}{4}a^{2}=\dfrac {1}{2}a*10\Rightarrow a=\dfrac {4*10}{2\sqrt{3}}=\dfrac {20\sqrt{3}}{3} $
Area of hexagon $6\left ( \dfrac {\sqrt{3}}{4}a^{2} \right )=6*\dfrac {\sqrt{3}}{4}\dfrac {20\sqrt{3}}{3}\dfrac {20\sqrt{3}}{3}=200\sqrt{3}$

Multiple choice maths measures and motion unit of area units of area units of area and volume

A Pizza Seller makes a circular pizza of perimeter $44cm$.Find its area in$m^2$

  1. $.144m^2$
  2. $.0154m^2$
  3. $.36m^2$
  4. $none$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Perimeter = 2 * pi * r = 44 cm. r = 44 / (2 * 3.14) = 7 cm. Area = pi * r^2 = 3.14 * 49 = 153.86 cm^2. Converting to m^2: 153.86 / 10,000 = 0.015386 m^2, which is approximately 0.0154 m^2.

Multiple choice maths how many squares area of rectangular paths comparing areas spaces and boundaries - 2

Find the area of a square inscribed in a circle of radius $\displaystyle 5\sqrt{2}$ cm (in $\displaystyle cm^{2}$)

  1. 75

  2. 100

  3. 125

  4. 150
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The diagonal of the square will be equal to the diameter of the circle.
So,diagonal of the square $ = 2 \times 5 \sqrt {2} = 10 \sqrt {2} $

Diagonal of a square $ = \sqrt {2} \times side $
So, $ 10 \sqrt {2} = \sqrt {2} \times side $
$ => Side  =  10  cm $

Area of the square $ = { side }^{ 2 } = { 10 }^{ 2 } = 100 $ sq cm

Multiple choice maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

A circle of radius $7\ cm$ is scaled $3$ times. Then the perimeter of the circle become:

  1. $3$ times the original perimeter
  2. $6$ times the original perimeter
  3. $9$ times the original perimeter

  4. Doesn't change
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Radius of circle $=7 \ \ cm$

Perimeter $=2\pi r=2\times \pi\times7=14\pi\ \ cm$
When scaled $3$ times
New radius $=3\times 7=21 \ \ cm$
New Perimeter $=2\pi r=2\times \pi\times21=42\pi\ \ cm$
Ratio of perimeters $=\dfrac{42\pi}{14\pi}=3$
So the perimeter becomes three times.

Multiple choice mathematics and statistics angle and their measurement degree measure of angle measure of angle radians or degrees

A unit radian is approximately equal to

  1. $57^{\circ} 17' 43"$
  2. $57^{\circ} 17' 45"$
  3. $57^{\circ} 17' 47"$
  4. $57^{\circ} 17' 49"$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
1 radian x 180 degrees per pi radians = 57.295779513082 degrees.

0.295779513082 degrees x 60 minutes per 1 degree = 17.74677078492 minutes.
0.74677078492 minutes x 60 seconds per 1 minute = 44.8062470952 seconds.

Answer : 57 degrees, 17.75 minutes or

57 degrees, 17 minutes, 45 seconds
Multiple choice mathematics and statistics angle and their measurement degree measure of angle measure of angle radians or degrees

The area of a sector of a circle of radius $7\ cm$ and central angle $120^{o}$ is 

  1. $152\ cm^{2}$
  2. $\dfrac{154}{3}\ cm^{2}$
  3. $\dfrac{128}{3}\ cm^{2}$
  4. $128\ cm^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
Area$=\cfrac { 120 }{ 360 } \times \pi { r }^{ 2 }$
$=\cfrac { \pi  }{ 3 } \times 7\times 7=49\times \cfrac { \pi  }{ 3 } $
$=49\times \cfrac { 22 }{ 7\times 3 } =\cfrac { 154 }{ 3 }cm^2$
Multiple choice maths circle and its elements angle subtended by arc sector of a circle arcs and sectors

$r$ is the radius and $l$  is the length of an arc. The area of a sector is ______.

  1. $\dfrac { 1 } { 2 } r l$
  2. $\dfrac { 3 } { 2 } r ^ { 2 } l$
  3. $\dfrac { 4 } { 3 } r l$
  4. $\dfrac { 3 } { 2 } r l$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\begin{array}{l} Area\, of\, a\, \sec  tor\, =\dfrac { 1 }{ 2 } { r^{ 2 } }\theta  \ =\dfrac { 1 }{ 2 } \times r\times r\theta  \ =\dfrac { 1 }{ 2 } \times r\times l \ Hence,\, option\, A\, is\, \, the\, \, correct\, \, answer. \end{array}$