Circles

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Q1. A circle has a radius of 3 m. What is the diameter? (2022)

Solution:

Diameter = 2 * radius = 2 * 3 m = 6 m.

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Q2. A circle has an area of 78.5 cm². What is the radius? (Use π = 3.14) (2022)

Solution:

Area = πr². Therefore, r² = Area / π = 78.5 cm² / 3.14 = 25. r = √25 = 5 cm.

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Q3. What is the radius of a circle if its circumference is 62.8 cm? (2022)

Solution:

Circumference = 2πr; 62.8 = 2πr; r = 10 cm.

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Q4. 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)

Solution:

Arc length = (θ/360) * 2πr = (60/360) * 2 * π * 5 = 5.24 cm.

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Q5. A circle has a radius of 12 cm. What is the diameter? (2020)

Solution:

Diameter = 2 * radius = 2 * 12 = 24 cm.

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Q6. What is the length of an arc of a circle with a radius of 4 cm and a central angle of 90 degrees? (2021)

Solution:

Arc length = (θ/360) * 2πr = (90/360) * 2π * 4 = 2π cm.

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Q7. If the radius of a circle is halved, how does the circumference change? (2022) 2022

Solution:

Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.

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Q8. What is the distance between the center of a circle and a point on its circumference if the radius is 10 cm? (2022)

Solution:

The distance from the center to a point on the circumference is the radius, which is 10 cm.

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Q9. A circle has an area of 154 cm². What is the radius? (2019) 2019

Solution:

Area = πr². Therefore, r = √(Area/π) = √(154/3.14) ≈ 7 cm.

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Q10. What is the area of a circle with a diameter of 16 cm? (Use π = 3.14) (2022)

Solution:

Radius = diameter/2 = 16 cm / 2 = 8 cm. Area = πr² = 3.14 * 8² = 201.06 cm².