Worksheet on Circle is a great resource for students to learn complete circle concepts in Math. Practice all the questions provided in the Circle Worksheet to score good marks in the exams. All questions including radius, diameter, Circumference, Area are given in this article.

Check out different ways to solve circle math problems in this article. The Circle Worksheet with Answers has questions on finding the circumference, area, identifying radius, chord, and diameter of a circle, etc. Download the Printable Worksheet on Circle in PDF Formats and practice the questions on a frequent basis and improve your proficiency in the concept.

Do Refer: Practice Test on Circle

1. Explain the following terms of a circle?
(ii) Centre
(iii) Chord
(iv) Diameter
(v) Interior of a Circle

Solution:

Radius – The radius is the line segment from the center of the circle to the circumference or surface of the circle.
Center – The Center of the circle is the middle point that is equidistant from all the points on the edge of the circle.
Chord – The chord on the circle that joins two points on the circumference.
Diameter – The diameter of the circle is defined as double the length of the radius of a circle.

2. The following figure shows a circle with center O and some line segments drawn in it. Classify the line segments as chord, radius, and diameter, etc.

(i) OM = ………………..
(ii) OL = ………………..
(iii) ON = ………………..
(iv) AB = ………………..
(v) CD = ………………..
(vi) EF = ………………..

Solution:

(iv) AB = Diameter
(v) CD = Chord
(vi) EF = Chord

3. Find the area and the circumference of a circle whose radius is 30 cm. (Take the value of π = 3.14)

Solution:

Given that the radius is 30 cm.
Area =πr2
Area =  3.14  × (30)2
Area =  2826 cm2
Circumference, C = 2πr
Circumference = 2 × 3.14 × 30
Circumference = 188.4 cm

4. Find the area of a circle whose circumference is 15.7 cm?

Solution:

Given that the circumference is 15.7 cm.
To find the area of a circle, we must find the radius.
From the circumference, the radius can be calculated
2 π r = 15.7
(2)(3.14)r = 15.7
r = $$\frac { 15.7 }{ (2)(3.14) }$$
r = $$\frac { 15.7 }{ 6.28 }$$
r = 2.5
Therefore, the radius of the circle is 2.5 cm.
The area of a circle is πr2 square units
Now, substitute the radius value in the area of a circle formula, we get
A = π(2.5)2
A = 3.14 x 6.25
A =  19.625 cm2

Therefore, the area of a circle is 19.625 cm2.

5. Observe the circles given below and identify them.

(b) Chord = …………………………
(c) Diameter = …………………………

Solution:

(a) Radius = OC, OD, OM
(b) Chord = EF, CN
(c) Diameter = CD

6. Take a point and draw a circle of radii 5 cm, 2 cm, 7 cm, each having the same center M.

Solution:

Given that three circles having a radius of 5 cm, 2 cm, 7 cm.
All 3 circles must have the same center named as M.
So, the figure with three different radii is given below.

7. Take two points Q and R on a circle. Draw a circle with Q in the center and passes through R.

Solution:

Given that two points Q and R are present on a circle.
Q is the center of the circle and it passes through R.
So, the figure with three different radii is given below.

8. To cover a distance of 5 km a wheel rotates 2500 times. Find the radius of the wheel?

Solution:

Given that a distance of 5 km a wheel rotates 2500 times.
No. of rotations = 2500.
Total distance covered = 5 km, and we have to find out the radius of the circle.
Let ‘r’ be the radius of the wheel.
Circumference of the wheel = Distance covered in 1 rotation = 2πr.
In 2500 rotations, the distance covered = 5 km = 500000 cm.
Hence, in 1 rotation, the distance covered = 500000 cm/2500 = 200cm
But this is equal to the circumference. Hence, 2πr = 200 cm
r = $$\frac { 200 }{ 2π }$$
r = $$\frac { 100 }{ π }$$
Taking the approximate value of π as 22/7, we get
r = 100 x 7/22
r = 31.82 cm approx.

9. The difference between the circumference and the diameter of a circular bangle is 10 cm. Find the radius of the bangle. (Take π = 22/7)

Solution:

Let the radius of the bangle be ’r’.
According to the question:
Circumference – Diameter = 10 cm
We know that the Circumference of a circle = 2πr
Diameter of a circle = 2r
Therefore, 2πr – 2r =10 cm
2r(π-1) = 10 cm
2r((22/7) – 1) = 10 cm
r($$\frac { 15 }{ 7 }$$) = 5 cm
r = 5 ($$\frac { 7 }{ 15 }$$)
r = 2.333 cm

The radius of the bangle is 2.333 cm.

10. Observe the circles given below and identify

Label the centre as O.
Draw 2 radius OA and OB.
Draw the chord CB.

Solution:

Given that the circle and point the centre as O. OA = OB = 2.
The CB is a chord.
The below figure shows the exact details of the given information.

11. Draw a diameter, radius, chord in the given circle using the points. Also, find the length of diameter and radius.
(i) Radius = ……………… = ……………… cm
(ii) Diameter = ……………… = ……………… cm
(iii) Highlight the circumference by using green color.
(iii) Highlight the chord by using blue color.

Solution:

Given that the circle and point the centre as O.
Let us consider the radius 2 cm.
OL and OM are the radii of the circle. LM is the diameter of the circle.
The MN and NL are the is a chord of the circle.
(i) OL = OM = 2 cm
(ii) LM = 4 cm = 2 (OL)
The below figure shows the exact details of the given information.

(i) 6 cm
(ii) 4 cm
having the same circle.

Solution:

Given that two circles with radii of 4 cm and 6 cm.
Both circles must have the same center.
Let the centre be X. Then, the first circle will have a radius of 4 cm. The second circle will have a radius of 6 cm.

13. Draw a circle of radius 5 cm.

Solution:

Take a Circle with centre O. Draw the radius of the circle 5 cm.
The radius of the circle is the line segment from the center to any point on the circumference.
Let the point be A.
OA = 5 cm.

14. Draw a circle of diameter 7.5 cm.

Solution:

Take a Circle with centre O. Draw the diameter of the circle 7.5 cm.
The diameter of the circle is defined as double the length of the radius of a circle.
Let the points of the diameter are A and B.
AB = 7.5 cm.

15. Draw a circle with centre M and radius 2.4 cm. Mark points A, B, C such that A lies in the interior of the circle, B lies on the circle and C lies in the exterior of the circle.

Solution:

Take a Circle with centre M. Draw the given points on the circle.
A lies inside the circle. B lies on the circle and C lies outside the circle.

16. Draw a circle whose diameter is 20 cm. Find its radius?

Solution:

Given that the diameter of the circle is 20 cm.
The diameter is double the length of the radius.
d = 2r where d is the diameter of the circle and r is the radius of the circle.
20 = 2r
r = 10 cm.
Therefore, the radius of the circle is 10 cm.

17. Find the radius if the diameter of the circle is:
(i) 6 cm
(ii) 16 cm
(iii) 14 m
(iv) 18 cm

Solution:

(i) Given that the diameter of the circle is 6 cm.
The diameter is double the length of the radius.
d = 2r where d is the diameter of the circle and r is the radius of the circle.
6 = 2r
r = 3 cm.
Therefore, the radius of the circle is 3 cm.

(ii) Given that the diameter of the circle is 16 cm.
The diameter is double the length of the radius.
d = 2r where d is the diameter of the circle and r is the radius of the circle.
16 = 2r
r = 8 cm.
Therefore, the radius of the circle is 8 cm.

(iii) Given that the diameter of the circle is 14 cm.
The diameter is double the length of the radius.
d = 2r where d is the diameter of the circle and r is the radius of the circle.
14 = 2r
r = 7 cm.
Therefore, the radius of the circle is 7 cm.

(iv) Given that the diameter of the circle is 18 cm.
The diameter is double the length of the radius.
d = 2r where d is the diameter of the circle and r is the radius of the circle.
18 = 2r
r = 9 cm.
Therefore, the radius of the circle is 9 cm.

18. Find the diameter if the radius of the circle is:
(i) 22 cm
(ii) 5 cm
(iii) 20 cm
(iv) 19 cm

Solution:

(i) Given that the radius of the circle is 22 cm.
The radius is half of the diameter of the circle.
d = 2r where d is the diameter of the circle and r is the radius of the circle.
d = 2r
d = 2 (22) cm.
d = 44 cm.
Therefore, the diameter of the circle is 44 cm.

(ii) Given that the radius of the circle is 5 cm.
The radius is half of the diameter of the circle.
d = 2r where d is the diameter of the circle and r is the radius of the circle.
d = 2r
d = 2 (5) cm.
d = 10 cm.
Therefore, the diameter of the circle is 10 cm.

(iii) Given that the radius of the circle is 20 cm.
The radius is half of the diameter of the circle.
d = 2r where d is the diameter of the circle and r is the radius of the circle.
d = 2r
d = 2 (20) cm.
d = 40 cm.
Therefore, the diameter of the circle is 40 cm.

(iv) Given that the radius of the circle is 19 cm.
The radius is half of the diameter of the circle.
d = 2r where d is the diameter of the circle and r is the radius of the circle.
d = 2r
d = 2 (19) cm.
d = 38 cm.
Therefore, the diameter of the circle is 38 cm.

19. With the same circle, draw three circles first with a radius of 3 cm. second with a radius of 5 cm, and third with a radius of 7 cm.

Solution:

Given that three circles having a radius of 3 cm, 5 cm, 7 cm.
All 3 circles must have the same center named as M.
So, the figure with three different radii is given below.

20. A circle has a radius 8 cm. Find the length of the longest chord of this circle?

Solution:

Given that a circle has a radius of 8 cm.
The longest chord of this circle is a diameter.
d = 2r where d is the diameter of the circle and r is the radius of the circle.
d = 2r
d = 2 (8) cm.
d = 16 cm.
Therefore, the diameter or the length of the longest chord of the given circle is 16 cm.