Practice Questions
Concept Explanation
A right circular cylinder has two parallel circular bases of radius r and height h. Use π = 22/7 unless noted.
Formulas
- Volume V = πr²h
- Curved surface area CSA = 2πrh
- Total surface area TSA = 2πr(r + h)
Example
r = 7 cm, h = 10 cm: V = (22/7) × 49 × 10 = 1540 cu cm.
Common Trap
Open cylindrical pipe/tank problems may use only CSA or subtract inner cylinder for material volume.
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Q1 EasyVolume of cylinder r = 7 cm, h = 10 cm (π = 22/7) is:ExplanationV = πr²h = (22/7) × 49 × 10 = 1540 cu cm. Hence the answer is 1540 cu cm.
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Q2 EasyCylinder diameter 14 cm, height 10 cm (π = 22/7). Volume:Explanationr = 7 cm, V = 1540 cu cm. Hence the answer is 1540 cu cm.
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Q3 EasyCSA of cylinder r = 7 cm, h = 5 cm (π = 22/7) is:ExplanationCSA = 2πrh = 2 × (22/7) × 7 × 5 = 220 sq cm. Hence the answer is 220 sq cm.
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Q4 EasyHollow cylinder r = 7 cm, h = 10 cm, metal thickness negligible. Volume (π = 22/7):ExplanationSolid cylinder volume = 1540 cu cm. Hence the answer is 1540 cu cm.
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Q5 MediumCSA 440 sq cm, height 10 cm (π = 22/7). Radius:Explanation2πrh = 440 gives r = 7 cm. Hence the answer is 7 cm.
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Q6 MediumRolling cylinder radius 7 cm completes 5 revolutions over 220 cm (π = 22/7). Distance per revolution:ExplanationDistance per revolution = circumference = 44 cm. Hence the answer is 44 cm.
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Q7 MediumTSA of cylinder r = 7 cm, h = 3 cm (π = 22/7) is:ExplanationTSA = 2πr(r + h) = 2 × (22/7) × 7 × (7 + 3) = 440 sq cm. Hence the answer is 440 sq cm.
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Q8 MediumCylinder volume 462 cu cm, r = 7 cm (π = 22/7). Height is:Explanationπr² = 154. h = 462 / 154 = 3 cm. Hence the answer is 3 cm.
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Q9 MediumCylinder height halved, radius doubled. Volume becomes:ExplanationV' = π(2r)²(h/2) = 2πr²h = 2V. Hence the answer is Double.
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Q10 MediumRatio of volumes of cylinders with radii 2 : 3 and equal heights is:ExplanationWith equal h, V ∝ r², so ratio = 2² : 3² = 4 : 9. Hence the answer is 4 : 9.
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Q11 MediumCylindrical can holds 1.54 L (π = 22/7), r = 7 cm. Height (1000 cu cm = 1 L):Explanation1540 cu cm = 1.54 L, so h = 10 cm. Hence the answer is 10 cm.
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Q12 HardTSA 748 sq cm, r = 7 cm (π = 22/7). Height:Explanation748 = 2 × (22/7) × 7 × (7 + h), so 748 = 44(7 + h), 7 + h = 17, h = 10 cm. Hence the answer is 10 cm.
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Q13 HardCylinder CSA 264 sq cm, r = 7 cm (π = 22/7). Height is:Explanation2πrh = 264, h = 264 / (2 × 22) = 6 cm. Hence the answer is 6 cm.
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Q14 HardTwo cylinders same volume, radii 7 cm and 14 cm. Ratio of heights h1 : h2:Explanationπr²h equal: h ∝ 1/r². Ratio = 14² : 7² = 4 : 1. Hence the answer is 4 : 1.
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DS1 Easy
What is the volume of the cylinder? (π = 22/7)
Statement IRadius is 7 cm and height is 10 cm.
Statement IIDiameter is 14 cm and height is 10 cm.
ExplanationEach gives r = 7, h = 10, V = 1540 cu cm. Answer: D. -
DS2 Easy
What is the total surface area? (π = 22/7)
Statement IRadius is 7 cm.
Statement IIHeight is 10 cm.
ExplanationNeed both r and h: TSA = 748 sq cm. Answer: C.
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DS3 Medium
What is the curved surface area? (π = 22/7)
Statement IRadius 7 cm, height 5 cm.
Statement IICSA is twice the area of a circle of radius 7 cm when height is 5 cm.
ExplanationStatement I alone: CSA = 220 sq cm. Statement II is descriptive but needs numeric link; I is direct. Answer: A. -
DS4 Medium
What is the height of the cylinder? (π = 22/7)
Statement IVolume is 1540 cu cm and radius is 7 cm.
Statement IITSA is 748 sq cm and radius is 7 cm.
ExplanationStatement I: h = 10 cm. Statement II: 748 = 44(7 + h), h = 10 cm. Each alone sufficient. Answer: D.