Area Related to Circles Class 10 MCQ Questions

Area Related to Circles Class 10 MCQ Questions are covered in this Article. Area Related to Circles Class 10 MCQ Test contains 30 questions. Answers to MCQs on Area Related to Circles Class 10 Maths are available at the end of the last question. MCQ Questions for Class 10 Maths with Answers have been made for Class 10 students to help check the concept you have learnt from detailed classroom sessions and application of your knowledge.

Board CBSE
Textbook Maths (NCERT)
Class Class 10
Chapter Chapter 12 Area Related to Circles
Category MCQ Questions for Class 10 Maths with Answers

Area Related to Circles Class 10 MCQ Questions

1. 2Ï€r of a circle is:

(a) Circumference

(b) Area

(c) Diameter

(d) segment

Answer

Answer: (a) Circumference

 

2. The value of π is

(a) 3.41

(b) 2.14

(c) 3.14

(d) 4.13

Answer

Answer: (c) 3.14

Explanation: π = 22/7 = 3.14

 

3. What is the relation of diameter with initial radius, if the radius of a circle is reduced by one fourth?

(a) d = 2r

(b) d = r/4

(c) d = 4r

(d) d = r/2

Answer

Answer: (d) d = r/2

Explanation: r2 = r1 /4
d =2 × r2
= 2 × r1/4
= r1/ 2




4. The circumference of a circle is

(a) Linear distance around the circle

(b) Length of complete arc of the circle

(c) Both

(d) None of the above

Answer

Answer: (c) Both

 

5. Odd one out

(a) Radius

(b) Diameter

(c) circumference

(d) diagonal

Answer

Answer: (d) diagonal

 

6. Find the area of the circle, when its circumference is 44cm.

(a) 144cm2

(b) 154cm2

(c) 44cm2

(d) 220cm2

Answer

Answer: (b) 154cm2

Explanation: Circumference = 2Ï€r
44 = 2Ï€r
r = 22 / π
Area = πr2 = π × 22/π × 22/π = 22 × 7 = 154cm2

 

7. Swapnil is celebrating his birthday with his four friends. The cake is circular in shape with radius 2.8cm. He cut the cake and distributed its equal parts among his friends. Find the area of the cake he distributed to each friend.

(a) 6.16 cm2

(b) 6.10 cm2

(c) 16.6 cm2

(d) 6.20 cm2

Answer

Answer: (a) 6.16 cm2

Explanation:


Angle at center = 360Ëš

Angle of sector of circle = 360 / 4 = 90Ëš

Area of the cake he distributed to each friend

= Area of sector of a circle

= θ/(360˚) x πr2

= (90Ëš)/(360Ëš) x 22/7 x 2.8 x 2.8

= 22 x 0.7 x 0.4= 6.16 cm2

 

Area Related to Circles Class 10 MCQ Questions

8. A part of a circle made of the arc of the circle along with its two radii is called as

(a) Circumference

(b) Sector

(c) Segment

(d) Area

Answer

Answer: (b) Sector

 

9. A region bounded by a chord of a circle and the intercepted arc of the circle is

(a) Circumference

(b) Sector

(c) Segment

(d) Area

Answer

Answer: (c) Segment

 

10. The circumference of a circle of area 5Ï€ cm2 is

(a) √5π cm

(b) 6Ï€ cm

(c) 2√5 cm

(d) 2√5π cm

Answer

Answer: (d) 2√5π cm

Explanation:
Area of circle = πr2
5π = πr2
r = √5 cm
Circumference of circle = 2πr = 2√5π cm

 

11. Two circles with the centers O and O’ touching each other internally at center . Find the ratios of their areas.

(a) 3:2

(b) 4:1

(c) 3:4

(d) 1:1

Answer

Answer: (b) 4:1

Explanation:


In larger circle, Area1 = πr² = π x 3 x3 = 9πcm²

In smaller circle, diameter = radius of larger circle = 3cm

Radius = 3 /2 = 1.5cm

Area2 = π x 1.5 x 1.5 = 2.25πcm²

A1: A2 = 9π: 2.25π = 4:1




12. Name 1 and 2 given in the figure

(a) Minor sector and major sector

(b) Major sector and minor sector

(c) Minor segment and major segment

(d) Major segment and minor segment

Answer

Answer: (b) Major sector and minor sector

 

13. Find the area of segment​

(a) 4.16cm2

(b) 14.6cm2

(c) 4.56cm2

(d) 4.78cm2

Answer

Answer: (c) 4.56cm2

Explanation:
Area of segment = Area of sector – Area of triangle

Area of sector = θ/(360˚) × πr2

= (90˚)/(360˚) × 22/7 × 4 × 4
= (3.14 × 4) cm2
= 12.56 cm2
Area of triangle AOB = 1/2 × base × height = 1/2 × 4×4 = 8cm2
(It is a right-angled triangle, ∠O = 90˚)
Area of segment = 12.56 – 8 = 4.56cm2

 

14. Find the perimeter of a circle, inscribing in a square of side 14cm.

(a) 44cm

(b) 65cm

(c) 40cm

(d) 52cm

Answer

Answer: (a) 44cm

Explanation:

Diameter of circle = side of square = 14cm
Radius = 14/2 = 7cm
Perimeter of circle = 2Ï€r
= 2 × 22/7 × 7
= 44cm

 

15. How many sectors can you draw in the circle having 60Ëš angle at center.

(a) 3

(b) 4

(c) 5

(d) 6

Answer

Answer: (d) 6

Explanation: There will be exactly 6 sectors in a circle having 60Ëš angle at center.
Angle at the center of circle = 360Ëš
For 6 sectors = 360 /6 = 60Ëš angle at center.

 

16. The ratio of the perimeters of the two circles in the figure is

(a) 1:1

(b) 1:2

(c) 1:3

(d) 1:4

Answer

Answer: (a) 1:1

Explanation:
diameter of both circles = breath of rectangle = 7cm

Radius of both circles = 7/2 = 3.5cm

Perimeter of C1: Perimeter of C2
= 2Ï€r1: 2Ï€r2
= r1: r2
= 3.5: 3.5
= 1:1

 

17. A line segment extending from the center of a circle to the circumference is

(a) Chord

(b) Tangent

(c) Radius

(d) Diameter

Answer

Answer: (c) Radius

 

18. Find the area of shaded region.

(a) 10.4cm2

(b) 10.5cm2

(c) 6.7cm2

(d) 7.2 cm2

Answer

Answer: (b) 10.5cm2

Explanation:
diameter of circle = side of square = 7cm
Radius = 7 /2 = 3.5cm
Area of shaded region = area of square – area of circle
= side × side – Ï€r2
= 7 ×7 – 22/7 × 3.5 × 3.5
= 49 – 38.5 = 10.5cm2

 

Area Related to Circles Class 10 MCQ Questions

19. If the area of circle is equal to its perimeter, find the radius of circle.

(a) 2

(b) 3

(c) 4

(d) 6

Answer

Answer: (a) 2

Explanation: Area of circle = Circumference of circle
Ï€r2 = 2Ï€r
r = 2

 

20. Any straight line drawn from the edge of a circle to another edge and passes through the center of the circle is

(a) Chord

(b) Tangent

(c) Radius

(d) Diameter

Answer

Answer: (d) Diameter

 

21. The line segment that joins two distinct points of a circle is

(a) Secant

(b) Tangent

(c) Chord

(d) Diameter

Answer

Answer: (c) Chord

 

22. As shown in figure, a circle is inscribed in a square of side 4cm. Find the length of an arc of a sector of the circle.

(a) 6cm

(b) 3.14cm

(c) 12.56cm

(d) None

Answer

Answer: (b) 3.14cm

Explanation: The diagonals of a square are equal and bisect each other at right angles. So, angle of sector of the circle = 90Ëš
Diameter of circle = side of square = 4cm
Radius = 4/2 = 2cm
Length of arc of sector of 90˚ = θ/(360˚) × 2πr
= (90˚)/(360˚) × 2 × 22/7 × 2
= 3.14 cm




23. Find the area of major sector of the circle of radius 7cm.

(a) 149 cm2

(b) 70 cm2

(c) 128.33 cm2

(d) 128 cm2

 

Answer

Answer: (c) 128.33 cm2

Explanation: Area of major sector = (360Ëš – θ)/(360Ëš) × Ï€r2
= (360Ëš – 60Ëš)/(360Ëš) × 22/7 × 7× 7
= (300˚)/(360˚) × 154
= 128.33cm2

 

24. Find the area of shaded region in the circle of radius 6cm and 3cm and having an angle of sector 60Ëš

(a) 1.56Ï€
(b)  4.5π
(c)  5π
(d)  9π

Answer

Answer: (b)  4.5π

Explanation: ∠AOB = 60°
Area of sector of big circle = A2 = ( θ)/(360˚) × πr²
= ( 60˚)/(360˚) × π × 6 × 6 = 6π
Area of sector of small circle = A1 = ( θ)/(360˚) × πr²
= ( 60˚)/(360˚) × π × 3 × 3 = 1.5π
Area of shaded region = A2 – A1
= 6Ï€ – 1.5Ï€ = 4.5Ï€

 

Area Related to Circles Class 10 MCQ Questions

25. A circle is drawn from one of the vertices of square of side 5cm. Find the area of shaded region.

(a) 37cm2

(b) 25cm2

(c) 50cm2

(d) None of the above

Answer

Answer: (d) None of the above

Explanation: In a square, all the sides are equal and each
angle is equal to 90Ëš
Angle of sector = 90Ëš
Area of shaded region = Area of major sector
= (360Ëš – θ)/(360Ëš) × Ï€r²
= (360Ëš – 90Ëš)/(360Ëš) × Ï€ × 4 × 4
= (270˚ )/(360˚) × 22/7 × 4 × 4
= 37.7cm²

 

26. The circumference of a circle is equal to area of square of side πcm. Find the ratio of radius of circle to side of square.

(a) 1:2

(b) 2:1

(c) π: 2

(d) 2: π

Answer

Answer: (a) 1:2

Explanation: circumference of a circle = area of square
2πr = side × side
2πr = π × π
r = π /2
r: π = 1:2

 

27. A sector of a circle of angle 270Ëš is inscribed in a square of side 8cm. Find the area of shaded region.

(a) 26cm2

(b) 32cm2

(c) 32cm2

(d) 64cm2

Answer

Answer: (c) 32cm2

Explanation:


Area of shaded region = Area of square – area of major sector
Radius of circle = d/2
= 8/2 = 4cm
Area of major sector = ( θ)/(360˚) × πr²
= ( 270˚)/(360˚) × π × 4 × 4
= 12π = 37.68cm²
Area of square = side × side
= 8 ×8 = 64cm²
Area of shaded region = 64 – 37.68
= 26.32cm²

 

 28. Find the length of arc of sector of a circle with 60˚ angle and 21cm of radius.

(a) 21cm

(b) 22cm

(c) 42cm

(d) 44cm

Answer

Answer: (b) 22cm

Explanation: Length of arc of sector of 60˚ = θ/(360˚) × 2πr
= (60˚)/(360˚) × 2 × 22/7 × 21
= 22 cm

 

29. Find the area of semi- circle, where circumference of circle is 22cm.

(a) 220cm2

(b) 420cm2

(c) 300cm2

(d) 19.25cm2

Answer

Answer: (d) 19.25cm2

Explanation:

Circumference = 2Ï€r

22 = 2× 22/7 × r

r = 7/2cm

= 3.5 cm

Area of semi circle = πr² / 2

= 22/7 × (3.5×3.5)/2

=19.25cm²

 

 30. The perimeter of a sector of circle with radius 14cm is 22cm. Find the area of sector.

(a) 154cm2

(b) 220cm2

(c) 440cm2

(d) 200cm2

Answer

Answer: (a) 154cm2

Explanation:

Length of arc of sector = θ/(360˚) × 2πr

22 = θ/(360˚) × 2 × 22/7 × 14

θ = 90˚

Area of sector = θ/(360˚) × πr²

= (90˚)/(360˚) × 22/7 x 14 x 14

= 154cm²

 

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