Practicing Areas Related to Circles Class 10 MCQs helps students improve mensuration understanding, circle-based calculations, and formula application skills for CBSE board exams. This chapter mainly focuses on sectors, segments, arc lengths, circumferences, and shaded region calculations, which are very important for competency-based and objective-type questions in the latest exam pattern. Many students find mensuration difficult because circular figures involve curved boundaries and multiple formulas together, but regular practice of Areas Related to Circles Class 10 MCQs with Answers helps improve calculation accuracy, figure interpretation, and problem-solving confidence naturally. The latest CBSE pattern now focuses more on conceptual understanding and application-oriented learning instead of direct memorization, which makes objective practice extremely important. Students preparing for board examinations can also explore MCQs, Class 10 MCQs, CBSE Board, and MCQs Class 10 Maths for chapter-wise practice based on the latest syllabus and board exam trends.
Why Areas Related to Circles is Important for Class 10 Students
The chapter Areas Related to Circles helps students understand how curved figures and circular regions are measured mathematically using formulas and geometrical reasoning.
This chapter is important because:
- Areas Related to Circles Class 10 MCQs are frequently asked in CBSE board exams
- Formula application skills improve significantly
- Students learn practical mensuration calculations
- Sector and arc understanding becomes stronger
- Shaded region problem-solving improves
- Competency-based objective questions are increasing
- Geometry visualization and analytical thinking improve naturally
Students who practice Areas Related to Circles MCQs Class 10 regularly usually solve mensuration problems more confidently in exams.
Important Concepts Covered in Areas Related to Circles Class 10 MCQs
Before solving Areas Related to Circles Class 10 MCQs with Answers, students should revise all important formulas and concepts carefully because most questions are directly formula and figure based.
Important concepts covered in this chapter include:
- Area of circle
- Circumference of circle
- Radius and diameter
- Sector of circle
- Segment of circle
- Arc length
- Semicircle
- Quadrant
- Central angle
- Shaded region calculations
- Circle-based mensuration formulas
- Curved boundary measurements
These concepts are very important for solving CBSE Areas Related to Circles Class 10 MCQs accurately.
Areas Related to Circles Class 10 MCQs with Answers
Practice important and exam-oriented Areas Related to Circles Class 10 MCQs designed according to the latest CBSE pattern and competency-based learning approach. These objective questions help students improve formula application, mensuration calculations, figure analysis, and board exam preparation skills effectively.
Q. The circumference of a circle is 88 cm. Find its radius.
A) 12 cm
B) 14 cm
C) 16 cm
D) 18 cm
Answer: B
Explanation:
Circumference = 2pi r
88 = 2 x (22/7) x r
88 = (44/7)r
r = 14 cm.
Q. Find the area of a sector of a circle with radius 14 cm and central angle 60 degree.
A) 154 sq cm
B) 308/3 sq cm
C) 616/3 sq cm
D) 462 sq cm
Answer: B
Explanation:
Area of sector = (theta/360) x pi r^2
= (60/360) x (22/7) x 14 x 14
= 308/3 sq cm.
Q. A wheel has radius 35 cm. How much distance will it cover in 20 revolutions?
A) 22 m
B) 44 m
C) 66 m
D) 88 m
Answer: B
Explanation:
Distance in one revolution = circumference
= 2 x (22/7) x 35 = 220 cm
Distance in 20 revolutions = 220 x 20 = 4400 cm = 44 m.
Q. Find the length of an arc subtending an angle 90 degree at the center of a circle of radius 21 cm.
A) 22 cm
B) 33 cm
C) 44 cm
D) 66 cm
Answer: B
Explanation:
Arc length = (90/360) x 2pi r
= (1/4) x 2 x (22/7) x 21
= 33 cm.
Q. The area of a circle is 616 sq cm. Find its radius.
A) 7 cm
B) 14 cm
C) 21 cm
D) 28 cm
Answer: B
Explanation:
Area = pi r^2
616 = (22/7)r^2
r^2 = 196
r = 14 cm.
Q. Find the area of a quadrant of radius 10 cm.
A) 25pi sq cm
B) 50pi sq cm
C) 75pi sq cm
D) 100pi sq cm
Answer: A
Explanation:
Area of quadrant = (1/4)pi r^2
= (1/4)pi x 10^2
= 25pi sq cm.
Q. The diameter of a circle is 28 cm. Find its circumference.
A) 44 cm
B) 66 cm
C) 88 cm
D) 176 cm
Answer: C
Explanation:
Circumference = pi d
= (22/7) x 28
= 88 cm.
Q. A sector has radius 7 cm and angle 180 degree. Find its area.
A) 49pi sq cm
B) 77 sq cm
C) 154 sq cm
D) 98 sq cm
Answer: B
Explanation:
Area of sector = (180/360) x pi x 7^2
= (1/2) x (22/7) x 49
= 77 sq cm.
Q. Find the area of a circle whose circumference is 44 cm.
A) 154 sq cm
B) 308 sq cm
C) 616 sq cm
D) 77 sq cm
Answer: A
Explanation:
2pi r = 44
2 x (22/7) x r = 44
r = 7 cm
Area = (22/7) x 7 x 7 = 154 sq cm.
Q. A minute hand of length 14 cm sweeps through 30 degree. Find the area swept.
A) 154/3 sq cm
B) 77/3 sq cm
C) 44 sq cm
D) 88 sq cm
Answer: A
Explanation:
Area swept = (30/360) x pi x 14^2
= (1/12) x (22/7) x 196
= 154/3 sq cm.
Q. Find the area of a semicircle of radius 21 cm.
A) 693 sq cm
B) 1386 sq cm
C) 346.5 sq cm
D) 231 sq cm
Answer: A
Explanation:
Area of semicircle = (1/2)pi r^2
= (1/2) x (22/7) x 21 x 21
= 693 sq cm.
Q. The radius of a circle is increased from 7 cm to 14 cm. The area becomes:
A) Double
B) Triple
C) Four times
D) Eight times
Answer: C
Explanation:
Area depends on r^2.
If radius doubles, area becomes 2^2 = 4 times.
Q. Find the perimeter of a semicircle of radius 14 cm.
A) 44 cm
B) 72 cm
C) 88 cm
D) 66 cm
Answer: B
Explanation:
Perimeter of semicircle = pi r + 2r
= (22/7) x 14 + 28
= 44 + 28
= 72 cm.
Q. The area of a circle is numerically equal to its circumference. Find the radius.
A) 1 unit
B) 2 units
C) 3 units
D) 4 units
Answer: B
Explanation:
pi r^2 = 2pi r
r = 2 units.
Q. A wire of length 88 cm is bent into the shape of a circle. Find its radius.
A) 7 cm
B) 14 cm
C) 21 cm
D) 28 cm
Answer: B
Explanation:
Circumference = 88 cm
2 x (22/7) x r = 88
r = 14 cm.
Q. Find the length of the arc of a sector with angle 120 degree and radius 14 cm.
A) 88/3 cm
B) 44/3 cm
C) 66 cm
D) 22 cm
Answer: A
Explanation:
Arc length = (120/360) x 2pi r
= (1/3) x 2 x (22/7) x 14
= 88/3 cm.
Q. The area of a circle inscribed in a square of side 14 cm is:
A) 49pi sq cm
B) 98pi sq cm
C) 154 sq cm
D) 196 sq cm
Answer: A
Explanation:
Diameter = side = 14 cm
Radius = 7 cm
Area = pi x 7^2 = 49pi sq cm.
Q. A circle has radius 10.5 cm. Find its circumference.
A) 44 cm
B) 55 cm
C) 66 cm
D) 77 cm
Answer: C
Explanation:
Circumference = 2pi r
= 2 x (22/7) x 10.5
= 66 cm.
Q. Find the area of the ring formed by two concentric circles of radii 14 cm and 7 cm.
A) 462 sq cm
B) 308 sq cm
C) 154 sq cm
D) 616 sq cm
Answer: A
Explanation:
Area of ring = pi(R^2 - r^2)
= (22/7)(196 - 49)
= (22/7) x 147
= 462 sq cm.
Q. A sector has area 154 sq cm and radius 14 cm. Find its central angle.
A) 45 degree
B) 60 degree
C) 90 degree
D) 120 degree
Answer: C
Explanation:
(Theta/360) x (22/7) x 14 x 14 = 154
Theta = 90 degree.
Q. Find the area of the largest circle that can fit inside a square of side 20 cm.
A) 100pi sq cm
B) 200pi sq cm
C) 400pi sq cm
D) 50pi sq cm
Answer: A
Explanation:
Diameter = side = 20 cm
Radius = 10 cm
Area = pi x 10^2 = 100pi sq cm.
Q. A circular path has outer radius 14 cm and inner radius 7 cm. Find its area.
A) 462 sq cm
B) 308 sq cm
C) 154 sq cm
D) 616 sq cm
Answer: A
Explanation:
Area = pi(R^2 - r^2)
= (22/7)(196 - 49)
= 462 sq cm.
Q. Find the circumference of a circle whose radius is 17.5 cm.
A) 88 cm
B) 99 cm
C) 110 cm
D) 121 cm
Answer: C
Explanation:
Circumference = 2 x (22/7) x 17.5
= 110 cm.
Q. The area of a sector with angle 45 degree and radius 28 cm is:
A) 308 sq cm
B) 616 sq cm
C) 154 sq cm
D) 462 sq cm
Answer: A
Explanation:
Area = (45/360) x (22/7) x 28 x 28
= 308 sq cm.
Q. Find the area of a circle whose diameter is 42 cm.
A) 1386 sq cm
B) 2772 sq cm
C) 693 sq cm
D) 462 sq cm
Answer: A
Explanation:
Radius = 21 cm
Area = (22/7) x 21 x 21
= 1386 sq cm.
Q. A clock minute hand is 21 cm long. Find the area swept in 10 minutes.
A) 231 sq cm
B) 154 sq cm
C) 77 sq cm
D) 462 sq cm
Answer: A
Explanation:
Angle swept in 10 min = 60 degree
Area = (60/360) x (22/7) x 21 x 21
= 231 sq cm.
Q. Find the length of an arc subtending 60 degree at the center of radius 21 cm.
A) 11 cm
B) 22 cm
C) 44 cm
D) 66 cm
Answer: B
Explanation:
Arc length = (60/360) x 2pi r
= (1/6) x 2 x (22/7) x 21
= 22 cm.
Q. The ratio of areas of two circles with radii 7 cm and 14 cm is:
A) 1:2
B) 1:4
C) 2:1
D) 4:1
Answer: B
Explanation:
Ratio of areas = r1^2 : r2^2
= 7^2 : 14^2
= 49 : 196
= 1 : 4.
Q. A circle and a square have equal perimeters. If the circle radius is 14 cm, find the side of the square.
A) 11 cm
B) 22 cm
C) 44 cm
D) 88 cm
Answer: B
Explanation:
Circumference of circle = 2 x (22/7) x 14 = 88 cm
Perimeter of square = 88 cm
Side = 88/4 = 22 cm.
Q. Find the area of a circle whose circumference is 132 cm.
A) 1386 sq cm
B) 693 sq cm
C) 346.5 sq cm
D) 462 sq cm
Answer: A
Explanation:
2pi r = 132
2 x (22/7) x r = 132
r = 21 cm
Area = (22/7) x 21 x 21
= 1386 sq cm.
Understanding Circular Regions and Measurements in Simple Language
In this chapter, students learn how different portions of a circle are measured mathematically.
A circle can be divided into multiple regions depending on angles and boundaries.
For example:
- a pizza slice represents a sector,
- a curved cut portion represents a segment,
- and a semicircle represents half of a complete circle.
- Students also learn how to calculate:
- area of circular regions,
- circumference,
- curved boundary lengths,
- and shaded portions inside figures.
The chapter becomes easier when students visualize circular regions carefully instead of memorizing formulas blindly.
Important Formulas Used in Areas Related to Circles Class 10 MCQs
The following formulas are extremely important for solving Areas Related to Circles MCQs Class 10 and board exam questions.
| Formula Name | Formula |
|---|---|
| Area of Circle | πr² |
| Circumference of Circle | 2πr |
| Area of Sector | (θ/360) × πr² |
| Arc Length | (θ/360) × 2πr |
| Area of Semicircle | (1/2) × πr² |
| Perimeter of Semicircle | πr + 2r |
Students should revise these formulas regularly because many Areas Related to Circles Class 10 objective questions are directly calculation based.
Important Terms Students Must Understand
The following terms are very important for solving Areas Related to Circles Class 10 MCQs with Answers.
| Term | Meaning |
|---|---|
| Radius | Distance from center to boundary |
| Diameter | Double of radius passing through center |
| Sector | Region enclosed by two radii and an arc |
| Segment | Region enclosed by chord and arc |
| Arc | Curved part of circle boundary |
| Circumference | Total boundary length of circle |
| Central Angle | Angle formed at center of circle |
Understanding these terms properly improves conceptual clarity and solving speed.
Instructions Before Solving Areas Related to Circles MCQs
- Read the figure carefully before applying formulas because many questions contain multiple circular regions together.
- Check whether the question uses radius or diameter because students often confuse both values.
- Use the correct value of π according to the question requirements.
- Identify sectors, arcs, segments, and shaded portions properly before calculation.
- Apply formulas step-by-step because curved measurements require accurate substitution.
- Convert units carefully whenever necessary because unit conversion mistakes are common in mensuration problems.
- Practice competency-based and application-oriented Areas Related to Circles Class 10 MCQs regularly because the latest CBSE pattern focuses heavily on conceptual understanding.
- Avoid rushing calculations because small simplification mistakes can affect the final answer completely.
Common Mistakes Students Make in Areas Related to Circles Questions
Many students lose marks in Areas Related to Circles Class 10 MCQs because of formula confusion and incorrect figure interpretation.
Some common mistakes include:
- Radius and diameter confusion
- Incorrect π substitution
- Wrong sector formula usage
- Arc length calculation mistakes
- Unit conversion errors
- Incorrect shaded region subtraction
- Simplification mistakes during calculations
Students should solve mensuration questions carefully instead of depending only on shortcuts.
Understanding Sectors, Segments, and Shaded Regions Visually
One of the most important skills in this chapter is understanding how circular regions are formed inside figures.
Students can improve figure interpretation by:
- Observing curved boundaries carefully
- Identifying sectors and segments properly
- Understanding central angles visually
- Comparing complete and partial circular regions
- Practicing shaded figure questions regularly
Once students become comfortable with figure observation and area relationships, solving Areas Related to Circles Class 10 MCQs with Answers becomes much easier.
Revision Notes for Areas Related to Circles Class 10 MCQs
Students should revise these important points regularly before exams:
- Radius is half of diameter
- Area of circle = πr²
- Circumference = 2πr
- Sector area depends on central angle
- Arc length measures curved boundary
- Diameter passes through center
- Figure observation improves calculation accuracy
- Formula substitution requires careful attention
Short revision sessions help improve retention and board exam confidence significantly.
Final Summary
Practicing Areas Related to Circles Class 10 MCQs with Answers is one of the best ways to improve mensuration understanding, geometry visualization, and calculation accuracy for Class 10 Maths. This chapter is highly formula-oriented because students must understand sectors, arcs, circular regions, and shaded area relationships together instead of focusing only on direct calculations. Students preparing for CBSE board exams should focus on formula clarity, figure interpretation, and regular objective practice to improve confidence and solving speed naturally. Consistent practice of Areas Related to Circles Class 10 MCQs helps students strengthen practical geometry understanding, analytical reasoning, mathematical accuracy, and overall board exam performance effectively.