Practice Questions
Concept Explanation
A circle is the set of points equidistant from the centre. Use π = 22/7 in placement numerics unless stated otherwise.
Key Formulas
- Circumference C = 2πr = πd
- Area A = πr²
- Length of arc = (θ/360°) × 2πr
- Area of sector = (θ/360°) × πr²
Example
Radius 7 cm: circumference = 2 × (22/7) × 7 = 44 cm; area = (22/7) × 49 = 154 sq cm.
Common Trap
Distinguish radius and diameter; many formulas use r, not d.
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Q1 EasyRadius 7 cm. Circumference (π = 22/7) is:ExplanationCircumference C = 2πr = 2 × (22/7) × 7 = 44 cm. Hence the answer is 44 cm.
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Q2 EasyCircumference of a circle of radius 7 cm (π = 22/7) is:ExplanationC = 2πr = 2 × (22/7) × 7 = 44 cm. Hence the answer is 44 cm.
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Q3 EasyArea of a circle of radius 7 cm (π = 22/7) is:ExplanationA = πr² = (22/7) × 7 × 7 = 154 sq cm. Hence the answer is 154 sq cm.
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Q4 EasyCircumference 44 cm (π = 22/7). Radius is:Explanation2πr = 44, r = 44 × 7 / 44 = 7 cm. Hence the answer is 7 cm.
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Q5 EasyDiameter of a circle is 14 cm. Its area (π = 22/7) is:Explanationr = 7 cm. Area = 154 sq cm. Hence the answer is 154 sq cm.
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Q6 MediumArea of circle diameter 28 cm (π = 22/7):Explanationr = 14. Area = (22/7) × 196 = 616 sq cm. Hence the answer is 616 sq cm.
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Q7 MediumA wire bent into a circle of radius 14 cm (π = 22/7). Wire length is:ExplanationWire length = circumference = 2 × (22/7) × 14 = 88 cm. Hence the answer is 88 cm.
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Q8 MediumWheel diameter 70 cm rolls 220 m (π = 22/7). Revolutions:ExplanationCircumference = 220 cm. Revolutions = 22000/220 = 100. Hence the answer is 100.
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Q9 MediumArea 154 sq cm (π = 22/7). Diameter is:Explanationπr² = 154, r = 7, d = 14 cm. Hence the answer is 14 cm.
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Q10 MediumArea of a sector of radius 7 cm and angle 90° (π = 22/7) is:ExplanationSector = (90/360) × πr² = (1/4) × 154 = 38.5 sq cm. Hence the answer is 38.5 sq cm.
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Q11 MediumSemicircle diameter 14 cm (π = 22/7). Perimeter of semicircle:ExplanationCurved part = πr = 22 cm; total = 22 + 14 = 36 cm. Hence the answer is 36 cm.
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Q12 HardArc length 22 cm on circle r = 21 cm (π = 22/7). Central angle is:ExplanationArc = (θ/360) × 2πr = 22. 2πr = 132, so θ/360 = 22/132 = 1/6, θ = 60°. Hence the answer is 60°.
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Q13 HardRing formed by circles r = 7 and r = 14 (π = 22/7). Area between:ExplanationDifference = π(14² − 7²) = (22/7) × 147 = 462 sq cm. Hence the answer is 462 sq cm.
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Q14 HardTwo circles have radii 3 cm and 4 cm. Ratio of their areas is:ExplanationArea ratio = r1² : r2² = 9 : 16. Hence the answer is 9 : 16.
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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.
ExplanationStatement I: area = 154 sq cm. Statement II: r = 7, area = 154 sq cm. Each alone sufficient. Answer: D. -
DS2 Easy
What is the area of the sector?
Statement IRadius is 7 cm and angle is 90° (π = 22/7).
Statement IIThe sector is one-fourth of the circle of radius 7 cm.
ExplanationBoth give sector area 38.5 sq cm. Each alone sufficient. Answer: D.
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DS3 Easy
What is the radius of the circle? (π = 22/7)
Statement IArea is 154 sq cm.
Statement IICircumference is 44 cm.
ExplanationEach gives r = 7 cm. Answer: D. -
DS4 Medium
What is the circumference? (π = 22/7)
Statement IDiameter is 14 cm.
Statement IIArea is 154 sq cm.
ExplanationStatement I: C = 44 cm. Statement II: r = 7, C = 44 cm. Each alone sufficient. Answer: D.