Q. A chord of a circle is 10 cm long and is 6 cm away from the center. What is the radius of the circle? (2023)
A.
8 cm
B.
10 cm
C.
12 cm
D.
14 cm
Show solution
Solution
Using Pythagoras theorem: r² = (10/2)² + 6²; r² = 25 + 36 = 61; r = √61 ≈ 10 cm.
Correct Answer:
B
— 10 cm
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Q. A chord of a circle is 12 cm long and is 5 cm away from the center. What is the radius of the circle? (2020)
A.
10 cm
B.
13 cm
C.
15 cm
D.
12 cm
Show solution
Solution
Using Pythagoras theorem: r² = (5)² + (6)² = 25 + 36 = 61; r = √61 ≈ 7.81 cm.
Correct Answer:
B
— 13 cm
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Q. A circle has a diameter of 10 cm. What is its circumference? (2022)
A.
31.4 cm
B.
20 cm
C.
15.7 cm
D.
25 cm
Show solution
Solution
Circumference = πd = π * 10 = 31.4 cm.
Correct Answer:
A
— 31.4 cm
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Q. A circle has a diameter of 20 cm. What is its circumference? (2022)
A.
62.8 cm
B.
40 cm
C.
31.4 cm
D.
20 cm
Show solution
Solution
Circumference = πd = π * 20 = 62.8 cm.
Correct Answer:
A
— 62.8 cm
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Q. A circle has a radius of 10 cm. What is the diameter? (2020)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Diameter = 2 * radius = 2 * 10 cm = 20 cm.
Correct Answer:
D
— 20 cm
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Q. A circle has a radius of 12 cm. What is the diameter? (2020)
A.
6 cm
B.
12 cm
C.
24 cm
D.
18 cm
Show solution
Solution
Diameter = 2 * radius = 2 * 12 = 24 cm.
Correct Answer:
C
— 24 cm
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Q. A circle has a radius of 3 cm. What is the diameter in millimeters? (2023)
A.
30 mm
B.
60 mm
C.
90 mm
D.
120 mm
Show solution
Solution
Diameter = 2 * radius = 2 * 3 cm = 6 cm = 60 mm.
Correct Answer:
A
— 30 mm
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Q. A circle has a radius of 3 m. What is the diameter? (2022)
A.
3 m
B.
6 m
C.
9 m
D.
12 m
Show solution
Solution
Diameter = 2 * radius = 2 * 3 m = 6 m.
Correct Answer:
B
— 6 m
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Q. A circle has a radius of 5 cm. What is the length of an arc that subtends a central angle of 60 degrees? (2021)
A.
5.24 cm
B.
10.47 cm
C.
3.14 cm
D.
6.28 cm
Show solution
Solution
Arc length = (θ/360) * 2πr; = (60/360) * 2π * 5 = 10.47 cm.
Correct Answer:
B
— 10.47 cm
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Q. A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 60 degrees at the center? (2020)
A.
5.24 cm
B.
3.14 cm
C.
5.00 cm
D.
10.47 cm
Show solution
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * π * 5 = 5.24 cm.
Correct Answer:
A
— 5.24 cm
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Q. A circle has a radius of 5 cm. What is the length of an arc that subtends an angle of 60 degrees? (2023)
A.
5.24 cm
B.
3.14 cm
C.
5.00 cm
D.
10.47 cm
Show solution
Solution
Arc length = (θ/360) × 2πr; = (60/360) × 2π × 5 ≈ 5.24 cm.
Correct Answer:
A
— 5.24 cm
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Q. A circle has an area of 154 cm². What is the radius? (2019)
A.
7 cm
B.
14 cm
C.
21 cm
D.
28 cm
Show solution
Solution
Area = πr². Therefore, r = √(Area/π) = √(154/3.14) ≈ 7 cm.
Correct Answer:
B
— 14 cm
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Q. A circle has an area of 154 cm². What is the radius? (2019) 2019
A.
7 cm
B.
14 cm
C.
21 cm
D.
28 cm
Show solution
Solution
Area = πr². Therefore, r = √(Area/π) = √(154/3.14) ≈ 7 cm.
Correct Answer:
B
— 14 cm
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Q. A circle has an area of 78.5 cm². What is its radius? (Use π = 3.14) (2019)
A.
5 cm
B.
7 cm
C.
10 cm
D.
12 cm
Show solution
Solution
Area = πr². Therefore, r² = Area / π = 78.5 cm² / 3.14 = 25. r = √25 = 5 cm.
Correct Answer:
B
— 7 cm
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Q. A circle has an area of 78.5 cm². What is the radius? (Use π = 3.14) (2022)
A.
5 cm
B.
7 cm
C.
10 cm
D.
12 cm
Show solution
Solution
Area = πr². Therefore, r² = Area / π = 78.5 cm² / 3.14 = 25. r = √25 = 5 cm.
Correct Answer:
B
— 7 cm
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Q. A circle is inscribed in a square of side 10 cm. What is the area of the circle? (Use π = 3.14) (2020)
A.
78.5 cm²
B.
50 cm²
C.
100 cm²
D.
25 cm²
Show solution
Solution
Radius of the circle = side/2 = 10 cm / 2 = 5 cm. Area = πr² = 3.14 * 5² = 78.5 cm².
Correct Answer:
A
— 78.5 cm²
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Q. A circle is inscribed in a square of side 10 cm. What is the area of the circle? (2019)
A.
78.5 cm²
B.
100 cm²
C.
50 cm²
D.
25 cm²
Show solution
Solution
Radius = 10/2 = 5 cm; Area = πr² = π * 5² = 78.5 cm².
Correct Answer:
A
— 78.5 cm²
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Q. A circle is inscribed in a square of side 8 cm. What is the area of the circle? (2022)
A.
50.24 cm²
B.
64 cm²
C.
25.12 cm²
D.
32 cm²
Show solution
Solution
Radius = 8/2 = 4 cm; Area = πr² = π * 4² = 50.24 cm².
Correct Answer:
A
— 50.24 cm²
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Q. If a circle has a circumference of 31.4 cm, what is its radius? (2022)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Circumference = 2πr; 31.4 = 2 * π * r; r = 31.4 / (2 * π) = 5 cm.
Correct Answer:
A
— 5 cm
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Q. If a circle has a circumference of 62.8 cm, what is its radius? (2018)
A.
10 cm
B.
20 cm
C.
15 cm
D.
5 cm
Show solution
Solution
Circumference = 2πr; 62.8 = 2 * π * r; r = 62.8 / (2 * π) = 10 cm.
Correct Answer:
A
— 10 cm
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Q. If a circle has a radius of 10 m, what is the diameter? (2021)
A.
5 m
B.
10 m
C.
20 m
D.
15 m
Show solution
Solution
Diameter = 2 * radius = 2 * 10 m = 20 m.
Correct Answer:
C
— 20 m
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Q. If a circle has a radius of 3 cm, what is its circumference? (Use π = 3.14) (2023)
A.
6.28 cm
B.
9.42 cm
C.
12.56 cm
D.
15.70 cm
Show solution
Solution
Circumference = 2πr = 2 * 3.14 * 3 = 18.84 cm.
Correct Answer:
C
— 12.56 cm
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Q. If a circle has a radius of 4 cm, what is its circumference? (Use π = 3.14) (2023)
A.
12.56 cm
B.
25.12 cm
C.
50.24 cm
D.
6.28 cm
Show solution
Solution
Circumference = 2πr = 2 * 3.14 * 4 cm = 25.12 cm.
Correct Answer:
A
— 12.56 cm
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Q. If a circle has a radius of 4 cm, what is its diameter? (2022)
A.
4 cm
B.
8 cm
C.
12 cm
D.
16 cm
Show solution
Solution
Diameter = 2 * radius = 2 * 4 cm = 8 cm.
Correct Answer:
B
— 8 cm
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Q. If a circle's radius is tripled, by what factor does the area increase? (2019)
Show solution
Solution
Area = πr²; If r is tripled, new area = π(3r)² = 9πr²; Factor = 9.
Correct Answer:
D
— 9
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Q. If a circle's radius is tripled, how does its area change? (2021)
A.
Increases by 3 times
B.
Increases by 6 times
C.
Increases by 9 times
D.
Remains the same
Show solution
Solution
Area = πr². If radius is tripled, new area = π(3r)² = 9πr², which is 9 times the original area.
Correct Answer:
C
— Increases by 9 times
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Q. If a circle's radius is tripled, how does its area change? (2023) 2023
A.
Increases by 3 times
B.
Increases by 6 times
C.
Increases by 9 times
D.
Remains the same
Show solution
Solution
Area = πr². If radius is tripled, new area = π(3r)² = 9πr², which is 9 times the original area.
Correct Answer:
C
— Increases by 9 times
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Q. If the area of a circle is 78.5 cm², what is the radius? (2021)
A.
5 cm
B.
7 cm
C.
10 cm
D.
6 cm
Show solution
Solution
Area = πr²; 78.5 = π * r²; r² = 78.5/π = 25; r = 5 cm.
Correct Answer:
B
— 7 cm
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Q. If the circumference of a circle is 31.4 cm, what is its radius? (2022)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Circumference = 2πr; 31.4 = 2 * π * r; r = 5 cm.
Correct Answer:
A
— 5 cm
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Q. If the circumference of a circle is 31.4 cm, what is the radius? (2020) 2020
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Circumference = 2πr. Therefore, r = Circumference / (2π) = 31.4 cm / (2 * 3.14) = 5 cm.
Correct Answer:
A
— 5 cm
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Showing 1 to 30 of 76 (3 Pages)
Circles MCQ & Objective Questions
Understanding circles is crucial for students preparing for various school and competitive exams. Circles are a fundamental concept in geometry, and mastering them can significantly enhance your problem-solving skills. Practicing MCQs and objective questions on circles not only helps in reinforcing your knowledge but also boosts your confidence in tackling important questions during exams.
What You Will Practise Here
Definitions and properties of circles
Formulas related to circumference and area
Chords, tangents, and secants
Angles subtended by chords and arcs
Circle theorems and their applications
Equations of circles in coordinate geometry
Real-life applications of circles in various fields
Exam Relevance
Circles are a significant topic in the mathematics syllabus for CBSE, State Boards, and competitive exams like NEET and JEE. Questions related to circles often appear in various formats, including direct problem-solving, theoretical explanations, and application-based scenarios. Students can expect to encounter MCQs that test their understanding of circle properties, theorems, and calculations involving radius and diameter.
Common Mistakes Students Make
Confusing the terms radius and diameter
Misapplying circle theorems in problem-solving
Overlooking the relationship between angles and arcs
Errors in calculating the area and circumference
Neglecting to visualize problems with diagrams
FAQs
Question: What is the formula for the circumference of a circle?Answer: The circumference of a circle is calculated using the formula C = 2πr, where r is the radius.
Question: How do I find the area of a circle?Answer: The area of a circle can be found using the formula A = πr², where r is the radius.
Question: Why are circle theorems important for exams?Answer: Circle theorems help in solving complex problems and are frequently tested in exams, making them essential for scoring well.
Now is the time to enhance your understanding of circles! Dive into our practice MCQs and test your knowledge to ensure you are well-prepared for your exams. Remember, consistent practice is the key to success!
