Q. If the diameter of a circle is 20 cm, what is its circumference? (2022)
A.
62.83 cm
B.
31.42 cm
C.
20 cm
D.
40 cm
Show solution
Solution
Circumference = πd; C = π * 20 ≈ 62.83 cm.
Correct Answer:
A
— 62.83 cm
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Q. If the radius of a circle is 4 cm, what is the length of a chord that is 3 cm from the center? (2014)
A.
5 cm
B.
6 cm
C.
7 cm
D.
8 cm
Show solution
Solution
Using Pythagoras theorem: chord length = 2√(r² - d²) = 2√(4² - 3²) = 2√(16 - 9) = 2√7 ≈ 5.29 cm.
Correct Answer:
A
— 5 cm
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Q. If the radius of a circle is decreased by 2 cm, how does the area change? (Original radius is 10 cm) (2021)
A.
Decreases by 12.56 cm²
B.
Decreases by 25.12 cm²
C.
Decreases by 31.4 cm²
D.
Decreases by 50.24 cm²
Show solution
Solution
Original area = π(10)² = 314 cm²; New area = π(8)² = 201.06 cm². Change = 314 - 201.06 = 112.94 cm².
Correct Answer:
B
— Decreases by 25.12 cm²
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Q. If the radius of a circle is decreased by 2 cm, how does the area change? (Use π = 3.14) (2020)
A.
Decreases by 12.56 cm²
B.
Decreases by 25.12 cm²
C.
Increases by 12.56 cm²
D.
Remains the same
Show solution
Solution
Area change = π[(r-2)² - r²] = π[-4r + 4] = 3.14 * (-4r + 4).
Correct Answer:
B
— Decreases by 25.12 cm²
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Q. If the radius of a circle is doubled, how does the area change? (2021)
A.
It doubles
B.
It triples
C.
It quadruples
D.
It remains the same
Show solution
Solution
Area = πr²; if r is doubled, area = π(2r)² = 4πr², so it quadruples.
Correct Answer:
C
— It quadruples
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Q. If the radius of a circle is halved, by what factor does the circumference decrease? (2020)
A.
1/2
B.
1/4
C.
1/3
D.
1/6
Show solution
Solution
Circumference = 2πr; If r is halved, new circumference = πr; Factor = 1/2.
Correct Answer:
A
— 1/2
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Q. If the radius of a circle is halved, how does the circumference change? (2021)
A.
Halved
B.
Remains the same
C.
Doubled
D.
Tripled
Show solution
Solution
Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.
Correct Answer:
A
— Halved
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Q. If the radius of a circle is halved, how does the circumference change? (2022) 2022
A.
Halved
B.
Remains the same
C.
Doubled
D.
Quadrupled
Show solution
Solution
Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.
Correct Answer:
A
— Halved
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Q. If the radius of a circle is tripled, by what factor does the area increase? (2021)
Show solution
Solution
Area increases by a factor of (3r)²/r² = 9.
Correct Answer:
C
— 9
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Q. If the radius of a circle is tripled, how does the area change? (2019)
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. What is the angle subtended at the center of a circle by an arc of length 5 cm if the radius is 10 cm? (2022)
A.
30 degrees
B.
60 degrees
C.
90 degrees
D.
45 degrees
Show solution
Solution
Arc length = (θ/360) * 2πr; 5 = (θ/360) * 2π * 10; θ = (5 * 360) / (20π) = 30 degrees.
Correct Answer:
B
— 60 degrees
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Q. What is the area of a circle with a circumference of 31.4 cm? (2020)
A.
25 cm²
B.
50 cm²
C.
75 cm²
D.
100 cm²
Show solution
Solution
Circumference = 2πr; 31.4 = 2πr; r = 5 cm; Area = πr² = 25 cm².
Correct Answer:
A
— 25 cm²
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Q. What is the area of a circle with a diameter of 10 cm? (2023)
A.
25π cm²
B.
50π cm²
C.
75π cm²
D.
100π cm²
Show solution
Solution
Radius = diameter/2 = 10/2 = 5 cm. Area = πr² = π(5)² = 25π cm².
Correct Answer:
A
— 25π cm²
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Q. What is the area of a circle with a diameter of 16 cm? (2023) 2023
A.
64π cm²
B.
32π cm²
C.
16π cm²
D.
8π cm²
Show solution
Solution
Radius = diameter/2 = 16/2 = 8 cm. Area = πr² = π(8)² = 64π cm².
Correct Answer:
A
— 64π cm²
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Q. What is the area of a circle with a diameter of 16 cm? (Use π = 3.14) (2022)
A.
201.06 cm²
B.
100.48 cm²
C.
50.24 cm²
D.
25.12 cm²
Show solution
Solution
Radius = diameter/2 = 16 cm / 2 = 8 cm. Area = πr² = 3.14 * 8² = 201.06 cm².
Correct Answer:
A
— 201.06 cm²
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Q. What is the area of a circle with a radius of 10 m? (2023)
A.
314 m²
B.
100 m²
C.
200 m²
D.
150 m²
Show solution
Solution
Area = πr² = π * 10² = 314 m².
Correct Answer:
A
— 314 m²
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Q. What is the area of a circle with a radius of 3 cm? (2021)
A.
28.26 cm²
B.
9.42 cm²
C.
12.56 cm²
D.
18.84 cm²
Show solution
Solution
Area = πr² = π * 3² = 28.26 cm².
Correct Answer:
C
— 12.56 cm²
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Q. What is the area of a circle with a radius of 3 m? (2020)
A.
28.26 m²
B.
9.42 m²
C.
18.84 m²
D.
12.56 m²
Show solution
Solution
Area = πr²; = π * 3² = 28.26 m².
Correct Answer:
A
— 28.26 m²
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Q. What is the area of a sector of a circle with a radius of 4 cm and a central angle of 90 degrees? (2014)
A.
6.28 cm²
B.
12.56 cm²
C.
3.14 cm²
D.
9.42 cm²
Show solution
Solution
Area of sector = (θ/360) * πr²; = (90/360) * π * 4² = 12.56 cm².
Correct Answer:
B
— 12.56 cm²
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Q. What is the area of a sector of a circle with a radius of 4 cm and an angle of 90 degrees? (2023)
A.
4π cm²
B.
2π cm²
C.
8π cm²
D.
6π cm²
Show solution
Solution
Area of sector = (θ/360) × πr²; = (90/360) × π(4)² = 2π cm².
Correct Answer:
B
— 2π cm²
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Q. What is the area of a sector of a circle with a radius of 7 cm and an angle of 90 degrees? (2022)
A.
38.5 cm²
B.
12.25 cm²
C.
15.4 cm²
D.
25.5 cm²
Show solution
Solution
Area of sector = (θ/360) * πr² = (90/360) * π * 7² = 38.5 cm².
Correct Answer:
A
— 38.5 cm²
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Q. What is the diameter of a circle if its area is 50π square units? (2017)
A.
10 units
B.
5 units
C.
20 units
D.
15 units
Show solution
Solution
Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2√50 ≈ 10 units.
Correct Answer:
A
— 10 units
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Q. What is the diameter of a circle if its area is 78.5 cm²? (2020)
A.
10 cm
B.
8 cm
C.
6 cm
D.
12 cm
Show solution
Solution
Area = πr²; 78.5 = π * r²; r² = 78.5/π; d = 2√(78.5/π) = 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the diameter of a circle with a radius of 9 cm? (2022)
A.
9 cm
B.
18 cm
C.
27 cm
D.
36 cm
Show solution
Solution
Diameter = 2 * radius = 2 * 9 cm = 18 cm.
Correct Answer:
B
— 18 cm
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Q. What is the diameter of a circle with an area of 50.24 cm²? (2019)
A.
8 cm
B.
10 cm
C.
12 cm
D.
14 cm
Show solution
Solution
Area = πr²; 50.24 = πr²; r² = 50.24/π; r ≈ 4 cm; Diameter = 2r = 8 cm.
Correct Answer:
B
— 10 cm
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Q. What is the diameter of a circle with an area of 50π square units? (2017)
A.
10 units
B.
5 units
C.
20 units
D.
15 units
Show solution
Solution
Area = πr²; 50π = πr²; r² = 50; r = √50; Diameter = 2√50 ≈ 10 units.
Correct Answer:
A
— 10 units
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Q. What is the diameter of a circle with an area of 78.5 cm²? (2018)
A.
10 cm
B.
8 cm
C.
6 cm
D.
12 cm
Show solution
Solution
Area = πr²; 78.5 = πr²; r² = 78.5/π; d = 2√(78.5/π) ≈ 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 8 cm? (2023)
A.
8 cm
B.
16 cm
C.
4 cm
D.
0 cm
Show solution
Solution
The distance from the center to a point on the circumference is the radius, which is 8 cm.
Correct Answer:
A
— 8 cm
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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 15 cm? (2014)
A.
15 cm
B.
30 cm
C.
10 cm
D.
5 cm
Show solution
Solution
The distance from the center to any point on the circumference is always the radius, which is 15 cm.
Correct Answer:
A
— 15 cm
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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 12 cm? (2022)
A.
6 cm
B.
12 cm
C.
18 cm
D.
24 cm
Show solution
Solution
The distance from the center to a point on the circumference is the radius, which is 12 cm.
Correct Answer:
B
— 12 cm
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Showing 31 to 60 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!
