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All questions of Areas Related to Circles for Class 10 Exam

The shaded part of the circle in the given figure represents a
​
  • a)
    semi-circle
  • b)
    Chord
  • c)
    Sector
  • d)
    Segment
Correct answer is option 'D'. Can you explain this answer?

Neer Shreyansh answered
¶¶ According to the arithmetic definition of segment.


•• segment is a area which is form when a chord joins two point of arc of a circle....


→→And here the shaded portion verif all the possible conditions of segment so we say that the shaded area is a segment.

§ That's all §
Clear all your doubts with EduRev

If the area of a circle is 154 cm2, then its perimeter is
  • a)
    11cm
  • b)
    22 cm
  • c)
    44 cm
  • d)
    55 cm
Correct answer is option 'C'. Can you explain this answer?

Vivek Rana answered
 Given area of circle=154
      ⇒area of circle=πr²
                             =22/7 ×7×7.
                             =154 
so radius of the circle=7cm
 perimeter of circle=2πr
                           =2 ×22/7×7
                           =44cm
⇒perimeter of the circle=44 cm.

The ratio of radii of two circles is in the ratio of 1:5. Calculate the ratio of their perimeters.​
  • a)
    1:2
  • b)
    1:5
  • c)
    1:6
  • d)
    1:8
Correct answer is option 'B'. Can you explain this answer?

Abhishek Anand answered
Let the radii of circles be R1 and R2

according to question,

R1/R2 = 1/5

therefore, R1 = R2/5

Also,

2πR1/2πR2

By Putting the value of R1 here we can write this like,

2πR2/5/ 2πR2

now 2π and 2π will be cancelled, and this will be left ->

R2/5 × 5/R2

After cancelling R2 and R2, 1/5 will be left

= 1:5

So, the ratio of 2πR1 / 2πR2 = 1:5

The perimeter of a protractor is
  • a)
    π + 2r
  • b)
    πr
  • c)
    πr + 2r
  • d)
    π + r
Correct answer is option 'C'. Can you explain this answer?

Bhavya Banerjee answered
Let radius of the protractor be r 
∴ Perimeter of protractor = Perimeter of semicircle + Diameter of semicircle ⇒ Perimeter of protractor = πr+2r

The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is​
  • a)
    56 cm
  • b)
    42 cm
  • c)
    28 cm 
  • d)
    16 cm
Correct answer is option 'C'. Can you explain this answer?

Amit Sharma answered
Diameter of first circle = d1 = 36 cm
Diameter of second circle = d2 = 20 cm
∴ Circumference of first circle = πd1 = 36π cm
Circumference of second circle = πd2 = 20π cm
Now, we are given that,
Circumference of circle = Circumference of first circle + Circumference of second circle
πD = πd1 + πd2
⇒ πD = 36π + 20π
⇒ πD = 56π ⇒ D = 56
⇒ Radius = 56/2 = 28 cm

The diameter of a wheel is 1.26 m. The distance travelled in 500 revolutions is
  • a)
    2670 m
  • b)
    2880 m
  • c)
    1980 m
  • d)
    1596 m
Correct answer is option 'C'. Can you explain this answer?

Akshay Nair answered
Diameter of circle =1.26m
travel distance=circumference of circle �500 revolution
circumference of circle = one relvolution
now,
according to questions (A.T.Q),
finding distance,
circumference of circle = 2πr
=2x22/7x(1.26/2)
=3.96
distance in 500 revolution = 3.96x500
=1980.00

The perimeter (in cm) of a square circumscribing a circle of radius a cm, is
  • a)
    8 a
  • b)
    4 a
  • c)
    2 a
  • d)
    16
Correct answer is option 'A'. Can you explain this answer?

Naina Chopra answered

Given: Radius of the circle = r = a cm
To find the perimeter of the square.
Since the diameter of the circle is equal to the side of the square, therefore, side of the square = 2r = 2a cm a
Now, the perimeter of the square = 4 � (Side)
Thus, the perimeter of the square = 4(2a) cm
= 8a cm

If the radius of a circle is increased by 100%, then its area is increased by
  • a)
    100%
  • b)
    300%
  • c)
    200%
  • d)
    400%
Correct answer is option 'B'. Can you explain this answer?

Harshitha Das answered
Area of the circle with radius r =πr2
Now, New Radius = r + 100% of r = r + r = 2r
∴ New Area = π(2r)2 - 4πr2
∴ Increased Area = 4πr2 -  πr2 = 3πr2
And Area increased in

Find the circumference of the circle, whose area is 144 cm2​
  • a)
    24 πcm
  • b)
    46 πcm
  • c)
    72 πcm
  • d)
    12 πcm
Correct answer is option 'A'. Can you explain this answer?

Anjana Khatri answered
 area = pi times the square of the radius 
so the radius is the square root of 144, or 12cm 
circumference is pi times twice the radius, so it would be 24 pi cm

If the perimeter of a sector of a circle of radius 5.2 cm. is 16.4 cm. What multiple of the radius is the area of the sector?​
  • a)
    5th
  • b)
    3rd
  • c)
    4th
  • d)
    2nd
Correct answer is option 'B'. Can you explain this answer?

Nisha Choudhury answered
Let AOB be the given sector.
Given, 
Radius of circle r = 5.2 cm
Perimeter of sector AOB = 16.4 cm
So, OA + OB + Arc AB = 16.4 cm
5.2 + 5.2 + Arc AB = 16.4 cm
Arc AB = 6 cm
l = Arc length AB
= 6 cm
Area of sector AOB = 1/2 * r * l
= 1 / 2 * 5.2 x 6
= 15.6 cm^2 Ans.

The diameter of a wheel is 1 m. The number of revolutions it will make to travel a distance of 22 km will be
  • a)
    2,800
  • b)
    4,000
  • c)
    5,500
  • d)
    7,000
Correct answer is option 'D'. Can you explain this answer?

Khushi Pandey answered
Here is the solution to your question: 

So, the Correct Answer is Option D 

P.S. Cover everything related to the chapter Circles of Class 10 Mathematics by going through the link: 
Circles

If the difference between the circumference and the radius of a circle is 37 cm, then using π = 22/7, the circumference (in cm) of the circle is:​
  • a)
    44
  • b)
    7
  • c)
    14
  • d)
    154
Correct answer is option 'A'. Can you explain this answer?

Adidev Nair answered
Let r be the radius of circle.

Difference between circumference and radius of circle = 37 cm

Circumference of circle = 2
r

                                      = 2 x 22/7 x r = 44/7 x r

Now,

Difference between circumference and radius of circle = 2
r - r

37 = 44/7 x r - r

37 = r(44/7-1)

37 = r(44 - 7)/7

37 = 37 / 7 x r

37 x 7/37 = r

r = 7 cm

Now , Circumference of circle = 44/7 x r

                                                 = 44/7 x 7

                                                 = 44 cm . 

∴ Circumference of circle = 44 cm

If the diameter of semicircular protractor is 14 cm, then its perimeter is:​
  • a)
    30 cm
  • b)
    36 cm
  • c)
    44 cm
  • d)
    40 cm
Correct answer is option 'B'. Can you explain this answer?

Gaurav Kumar answered
Diameter=14, Radius=d/2=14/2=7cm
Perimeter of the semi- circle= Boundary of the semi-circle =Circumference of the semi-circle +Diameter= πr+D=

The area of a circle with diameter 6 m exceeds the combined areas of circles with diameters 4m and 2 m by​
  • a)
    5π m2
  • b)
    0 m2
  • c)
    π m2
  • d)
    4π m2
Correct answer is option 'D'. Can you explain this answer?

Pardeep Singh answered
R=d/2=6/2=3cm area of circle1=πr² =9πcm² ......(1) R=d/2=4/2=2cm area of circle2=πr² =4πcm² R=d/2=2/2=1cm area of circle=πr² =πcm² now add area of circle 2and3 =4π+π =5π........(2) now sub 2 from 1 =9π-5π =4πcm²

If C is the circumference of a circle of radius r, then perimeter of one of the quadrants will be​
  • a)
    C/2
  • b)
    C/4+r
  • c)
    C/4
  • d)
    C/4+2r
Correct answer is option 'D'. Can you explain this answer?

Adithya Shasan answered
Circumference = 2Πr
radius = r 
Perimeter of quadrant = 2r + 2Πr/4
                                    = 2r + C/4
                                    = C/4 + 2r
Therefore, Correct answer is option 'D'.

The perimeter (in cm) of a square circumscribing a circle of radius a cm, is​
  • a)
    8 a
  • b)
    2 a
  • c)
    16 a
  • d)
    4 a
Correct answer is option 'A'. Can you explain this answer?

Learning Education answered
Let ABCD is a square circumscribing a circle of radius a cm.
The side of square ABCD = Diameter of circle
⇒AB=2a
Therefore, perimeter of square AB=4×AB=4×2a=8 cm

A garden roller has a circumference of 4 m. The number of revolutions it makes in moving 40 metres are:
  • a)
    12
  • b)
    16
  • c)
    8
  • d)
    10
Correct answer is option 'D'. Can you explain this answer?

Avinash Patel answered
We have circumference which is equal to the boundary of the circle. So we have one revolution equal to circumference of the circle which is equal to 4
Distance covered by the roller=circumference of the roller*number of revolutions
⇒ number of revolutions = distance covered by the roller/circumference of the roller
= 40/4 = 10

If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius R, then
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?

Ananya Das answered
Area of circle with radius R1 = πR12
Area of circle with radius R2 = πR22
Area of circle with radius R = πR2
Area of circle with radius R1+Area of circle with radius R2 =Area of circle with radius R
πR12 + πR22=πR2
R12+R22=R2

A wire is bent in the form of a circle of radius 28 cm. It is bent to form a square. The length of the side of the square will be​
  • a)
    44 cm
  • b)
    40 cm
  • c)
    88 cm
  • d)
    30 cm
Correct answer is option 'A'. Can you explain this answer?

Gaurav Kumar answered
Circumference of a circle = 2πr
= 2*22/7*28
= 2*22*4
= 176
now, perimeter of square = circumference of a circle = 176
Therefore, side of square = perimeter/4
= 176/4
= 44 answer.

The radius of a circle if its perimeter and area are numerically equal is​
  • a)
    8 units
  • b)
    5 units
  • c)
    2 units
  • d)
    4 units
Correct answer is option 'C'. Can you explain this answer?

Ananya Das answered
The perimeter of a circle is 2πr where r is the radius of the circle.
And it's area is πr^2

If area = perimeter

Then,

2πr = πr^2

2 = πr^2 / πr = r

Therefore, if r is 2units then the area and perimeter of the circle would be numerically equal.

If the area of a circle is equal to the area of a square, then the ratio of their perimeters is
  • a)
    π : 2
  • b)
    1 : 2
  • c)
    2 : π
  • d)
    √π : 2
Correct answer is option 'D'. Can you explain this answer?

Leelu Bhai answered
Acc. to ques,...

⇒ πr² = a²
⇒ r/a = 1/√π

now, ratio of perimeter = 2πr/4a
⇒ ratio = 2π/4√π = √π/2 or √π : 2

hence, D option is correct.

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is​
  • a)
    50 cm
  • b)
    31 cm
  • c)
    62 cm
  • d)
    25 cm
Correct answer is option 'A'. Can you explain this answer?

Mohini iyer answered
Given:
Radius of first circle = 24 cm
Radius of second circle = 7 cm

We need to find the diameter of a circle whose area is equal to the sum of the areas of the two circles.

Formula for the area of a circle:
Area = πr^2

Let's calculate the areas of the two circles first.

Area of the first circle = π(24)^2
= 576π cm^2

Area of the second circle = π(7)^2
= 49π cm^2

Now, we need to find the diameter of a circle whose area is equal to the sum of the areas of the two circles.

Sum of the areas of the two circles = 576π + 49π
= 625π cm^2

To find the diameter, we can use the formula for the area of a circle:

Area = πr^2

Let's substitute the given area into the formula:

625π = πr^2

Dividing both sides by π:

625 = r^2

Taking the square root of both sides:

r = √625
r = 25 cm

Since the radius is 25 cm, the diameter will be twice the radius:

Diameter = 2r
= 2(25)
= 50 cm

Therefore, the diameter of the circle whose area is equal to the sum of the areas of the two circles is 50 cm, which corresponds to option A.

Chapter doubts & questions for Areas Related to Circles - Mathematics (Maths) Class 10 2025 is part of Class 10 exam preparation. The chapters have been prepared according to the Class 10 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 10 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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