Practice Questions
Concept Explanation
A circle is the set of points equidistant from a centre. Key measures: radius (r), diameter (d = 2r).
Key Formulas
- Area = πr²
- Circumference = 2πr = πd
- Length of arc = (θ/360°) × 2πr
- Area of sector = (θ/360°) × πr²
Units
Use cm or m for radius; sq cm or sq m for area. Take π = 22/7 or 3.14 as stated in the question.
Example
Radius 7 cm, π = 22/7: Area = 154 sq cm, Circumference = 44 cm.
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Q1 Easy
Radius 7 cm, π = 22/7. Area of circle is:
ExplanationArea = 22/7 × 49 = 154 sq cm. -
Q2 Easy
Radius 7 cm, π = 22/7. Circumference is:
ExplanationCircumference = 2 × 22/7 × 7 = 44 cm. -
Q3 Easy
Diameter of a circle is 14 cm, π = 22/7. Area is:
Explanationr = 7 cm. Area = 154 sq cm. -
Q4 Medium
Radius 14 cm, π = 22/7. Circumference is:
ExplanationCircumference = 2 × 22/7 × 14 = 88 cm. -
Q5 Medium
Radius 5 cm, π = 3.14. Area is:
ExplanationArea = 3.14 × 25 = 78.5 sq cm. -
Q6 Medium
Radius 5 cm, π = 3.14. Circumference is:
ExplanationCircumference = 2 × 3.14 × 5 = 31.4 cm. -
Q7 Medium
Circumference is 44 cm, π = 22/7. Radius is:
Explanation2 × 22/7 × r = 44, so r = 7 cm.
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Q8 Medium
Area is 154 sq cm, π = 22/7. Radius is:
Explanation22/7 × r² = 154, so r = 7 cm. -
Q9 Hard
A semicircle has radius 7 cm, π = 22/7. Perimeter (curved + diameter) is:
ExplanationCurved part = 22 cm, diameter = 14 cm. Total = 36 cm. -
Q10 Hard
Central angle 90°, radius 14 cm, π = 22/7. Arc length is:
ExplanationArc = 90/360 × 88 = 22 cm. -
Q11 Hard
Central angle 60°, radius 21 cm, π = 22/7. Area of sector is:
ExplanationSector = 60/360 × 22/7 × 441 = 231 sq cm. -
Q12 Easy
Diameter is 10 cm, π = 3.14. Area is:
Explanationr = 5 cm. Area = 3.14 × 25 = 78.5 sq cm. -
Q13 Medium
Two circles have radii 3 cm and 5 cm. Ratio of their areas is:
ExplanationArea ratio = r² ratio = 9 : 25. -
Q14 Hard
A wire 44 cm long (π = 22/7) is bent into a circle. Its radius is:
Explanation2 × 22/7 × r = 44, so r = 7 cm.
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DS1 Easy
What is the area of the circle? (π = 22/7)
Statement IRadius is 7 cm.
Statement IICircumference is 44 cm.
ExplanationEach alone gives r = 7 cm and area = 154 sq cm. -
DS2 Easy
What is the radius of the circle? (π = 3.14)
Statement IArea is 78.5 sq cm.
Statement IICircumference is 31.4 cm.
ExplanationEach alone gives r = 5 cm.
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DS3 Medium
What is the circumference? (π = 22/7)
Statement IDiameter is 14 cm.
Statement IIArea is 154 sq cm.
ExplanationEach alone gives r = 7 cm and circumference = 44 cm. -
DS4 Hard
What is the arc length of a 120° sector? (π = 22/7)
Statement IRadius is 21 cm.
Statement IICircumference of the circle is 132 cm.
ExplanationEach alone gives arc length = 44 cm.