Circles
Q. If the radius of a circle is tripled, by what factor does the area increase? (2021)
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)
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A.
Increases by 3 times
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B.
Increases by 6 times
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C.
Increases by 9 times
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D.
Remains the same
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)
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A.
30 degrees
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B.
60 degrees
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C.
90 degrees
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D.
45 degrees
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)
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A.
25 cm²
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B.
50 cm²
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C.
75 cm²
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D.
100 cm²
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)
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A.
25π cm²
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B.
50π cm²
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C.
75π cm²
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D.
100π cm²
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
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A.
64π cm²
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B.
32π cm²
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C.
16π cm²
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D.
8π cm²
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)
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A.
201.06 cm²
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B.
100.48 cm²
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C.
50.24 cm²
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D.
25.12 cm²
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)
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A.
314 m²
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B.
100 m²
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C.
200 m²
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D.
150 m²
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)
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A.
28.26 cm²
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B.
9.42 cm²
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C.
12.56 cm²
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D.
18.84 cm²
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)
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A.
28.26 m²
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B.
9.42 m²
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C.
18.84 m²
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D.
12.56 m²
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)
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A.
6.28 cm²
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B.
12.56 cm²
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C.
3.14 cm²
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D.
9.42 cm²
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)
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A.
4π cm²
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B.
2π cm²
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C.
8π cm²
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D.
6π cm²
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)
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A.
38.5 cm²
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B.
12.25 cm²
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C.
15.4 cm²
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D.
25.5 cm²
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)
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A.
10 units
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B.
5 units
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C.
20 units
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D.
15 units
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)
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A.
10 cm
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B.
8 cm
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C.
6 cm
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D.
12 cm
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)
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A.
9 cm
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B.
18 cm
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C.
27 cm
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D.
36 cm
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)
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A.
8 cm
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B.
10 cm
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C.
12 cm
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D.
14 cm
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)
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A.
10 units
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B.
5 units
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C.
20 units
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D.
15 units
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)
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A.
10 cm
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B.
8 cm
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C.
6 cm
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D.
12 cm
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)
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A.
8 cm
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B.
16 cm
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C.
4 cm
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D.
0 cm
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 12 cm? (2022)
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A.
6 cm
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B.
12 cm
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C.
18 cm
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D.
24 cm
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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Q. What is the distance between the center of a circle and a point on its circumference if the radius is 10 cm? (2022)
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A.
5 cm
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B.
10 cm
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C.
15 cm
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D.
20 cm
Solution
The distance from the center to a point on the circumference is the radius, which is 10 cm.
Correct Answer: B — 10 cm
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Q. What is the length of a chord that is 6 cm away from the center of a circle with a radius of 10 cm? (2015)
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A.
8 cm
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B.
12 cm
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C.
10 cm
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D.
6 cm
Solution
Using Pythagoras: (radius)² = (distance from center)² + (half chord)²; 10² = 6² + (half chord)²; half chord = 8 cm, so full chord = 16 cm.
Correct Answer: A — 8 cm
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Q. What is the length of a chord that is 6 cm from the center of a circle with a radius of 10 cm? (2019)
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A.
8 cm
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B.
12 cm
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C.
10 cm
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D.
6 cm
Solution
Using Pythagoras: chord length = 2√(r² - d²) = 2√(10² - 6²) = 2√(100 - 36) = 2√64 = 16 cm.
Correct Answer: A — 8 cm
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Q. What is the length of a diameter of a circle with a radius of 7 cm? (2022)
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A.
14 cm
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B.
21 cm
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C.
7 cm
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D.
28 cm
Solution
Diameter = 2 × radius; Diameter = 2 × 7 cm = 14 cm.
Correct Answer: A — 14 cm
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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (2021)
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A.
10.47 cm
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B.
12.57 cm
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C.
15.71 cm
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D.
20.94 cm
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.
Correct Answer: B — 12.57 cm
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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (2021) 2021
-
A.
10.47 cm
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B.
15.71 cm
-
C.
20.94 cm
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D.
25.13 cm
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.
Correct Answer: A — 10.47 cm
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Q. What is the length of an arc of a circle with a radius of 10 cm and a central angle of 60 degrees? (Use π = 3.14) (2023)
-
A.
10.47 cm
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B.
15.71 cm
-
C.
20.94 cm
-
D.
25.13 cm
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2 * 3.14 * 10 = 10.47 cm.
Correct Answer: A — 10.47 cm
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Q. What is the length of an arc of a circle with a radius of 4 cm and a central angle of 90 degrees? (2021)
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A.
2π cm
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B.
4π cm
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C.
π cm
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D.
8 cm
Solution
Arc length = (θ/360) * 2πr = (90/360) * 2π * 4 = 2π cm.
Correct Answer: A — 2π cm
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Q. What is the length of an arc of a circle with a radius of 5 cm and a central angle of 60 degrees? (2020)
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A.
5.24 cm
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B.
3.14 cm
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C.
5.00 cm
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D.
10.47 cm
Solution
Arc length = (θ/360) * 2πr = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.
Correct Answer: A — 5.24 cm
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