Circles
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)
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A.
10 cm
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B.
13 cm
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C.
15 cm
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D.
12 cm
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 20 cm. What is its circumference? (2022)
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A.
62.8 cm
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B.
40 cm
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C.
31.4 cm
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D.
20 cm
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)
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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
Diameter = 2 * radius = 2 * 10 cm = 20 cm.
Correct Answer: D — 20 cm
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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)
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A.
5.24 cm
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B.
10.47 cm
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C.
3.14 cm
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D.
6.28 cm
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)
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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) * 2 * π * 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) 2019
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A.
7 cm
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B.
14 cm
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C.
21 cm
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D.
28 cm
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)
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A.
5 cm
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B.
7 cm
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C.
10 cm
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D.
12 cm
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
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B.
7 cm
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C.
10 cm
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D.
12 cm
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? (2019)
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A.
78.5 cm²
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B.
100 cm²
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C.
50 cm²
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D.
25 cm²
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 10 cm. What is the area of the circle? (Use π = 3.14) (2020)
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A.
78.5 cm²
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B.
50 cm²
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C.
100 cm²
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D.
25 cm²
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 8 cm. What is the area of the circle? (2022)
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A.
50.24 cm²
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B.
64 cm²
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C.
25.12 cm²
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D.
32 cm²
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)
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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
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 radius of 3 cm, what is its circumference? (Use π = 3.14) (2023)
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A.
6.28 cm
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B.
9.42 cm
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C.
12.56 cm
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D.
15.70 cm
Solution
Circumference = 2πr = 2 * 3.14 * 3 = 18.84 cm.
Correct Answer: C — 12.56 cm
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Q. If a circle's radius is tripled, how does its area change? (2021)
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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. If a circle's radius is tripled, how does its area change? (2023) 2023
-
A.
Increases by 3 times
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B.
Increases by 6 times
-
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. If the circumference of a circle is 31.4 cm, what is its radius? (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
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
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B.
10 cm
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C.
15 cm
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D.
20 cm
Solution
Circumference = 2πr. Therefore, r = Circumference / (2π) = 31.4 cm / (2 * 3.14) = 5 cm.
Correct Answer: A — 5 cm
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Q. If the diameter of a circle is 20 cm, what is its circumference? (2022)
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A.
62.83 cm
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B.
31.42 cm
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C.
20 cm
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D.
40 cm
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 doubled, how does the area change? (2021)
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A.
It doubles
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B.
It triples
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C.
It quadruples
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D.
It remains the same
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, how does the circumference change? (2021)
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A.
Halved
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B.
Remains the same
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C.
Doubled
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D.
Tripled
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
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B.
Remains the same
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C.
Doubled
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D.
Quadrupled
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)
Solution
Area increases by a factor of (3r)²/r² = 9.
Correct Answer: C — 9
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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)
-
A.
28.26 m²
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B.
9.42 m²
-
C.
18.84 m²
-
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 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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