Practice Questions
Concept Explanation
A sphere is the set of points at distance r from the centre. A hemisphere is half a sphere plus the circular base. Use π = 22/7.
Formulas
- Sphere volume V = (4/3)πr³; surface area SA = 4πr²
- Hemisphere volume = (2/3)πr³
- Hemisphere CSA (curved) = 2πr²; TSA = 3πr²
Example
r = 7 cm: sphere volume = (4/3) × (22/7) × 343 = 1437⅓ cu cm; SA = 616 sq cm.
Common Trap
Hemisphere TSA includes the flat circular base (πr²).
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Q1 EasySurface area of sphere radius 7 cm (π = 22/7) is:ExplanationSA = 4πr² = 4 × (22/7) × 49 = 616 sq cm. Hence the answer is 616 sq cm.
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Q2 EasySpherical ball diameter 14 cm (π = 22/7). Surface area:Explanationr = 7, SA = 616 sq cm. Hence the answer is 616 sq cm.
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Q3 EasyCSA of hemisphere r = 7 cm (π = 22/7) is:ExplanationCSA = 2πr² = 308 sq cm. Hence the answer is 308 sq cm.
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Q4 EasyRatio of volumes of spheres radii 3 : 4 is:ExplanationV ∝ r³, ratio = 27 : 64. Hence the answer is 27 : 64.
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Q5 MediumHemispherical bowl r = 7 cm, full of water (π = 22/7). Volume of water:ExplanationHemisphere volume ≈ 718 cu cm. Hence the answer is 718 cu cm.
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Q6 MediumVolume of sphere radius 7 cm (π = 22/7) is:ExplanationV = (4/3) πr³ = (4/3) × (22/7) × 343 = 1437⅓ cu cm ≈ 1437 cu cm. Hence the answer is 1437 cu cm.
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Q7 MediumVolume of hemisphere radius 7 cm (π = 22/7) is:ExplanationV = (2/3) πr³ = (2/3) × 154 × 7 = 718⅔ cu cm ≈ 718 cu cm. Hence the answer is 718 cu cm.
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Q8 MediumHemisphere TSA 462 sq cm (π = 22/7). Radius:Explanation3πr² = 462, r = 7 cm. Hence the answer is 7 cm.
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Q9 MediumSphere volume 36π cu cm. Radius:Explanation(4/3)πr³ = 36π, r³ = 27, r = 3 cm. Hence the answer is 3 cm.
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Q10 MediumTSA of hemisphere r = 7 cm (π = 22/7) is:ExplanationTSA = 3πr² = 462 sq cm. Hence the answer is 462 sq cm.
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Q11 HardSphere and cube have equal surface area, sphere r = 7 cm (π = 22/7). Cube edge nearest:ExplanationSphere SA = 616. 6a² = 616, a = √102.67 ≈ 10.1 cm. Hence the answer is 10.2 cm.
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Q12 HardLead shot 44 identical spheres each r = 7 mm melted into cube (π = 22/7). Cube edge nearest (cm):ExplanationTotal sphere volume = 44 × (4/3)π(0.7)³ cu cm; approximate placement answer 1.4 cm edge. Hence the answer is 1.4 cm.
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Q13 HardHollow sphere outer r = 7 cm, inner r = 5 cm (π = 22/7). Material volume:ExplanationShell = (4/3)π(7³ − 5³) = (4/3) × (22/7) × 218 ≈ 704 cu cm. Hence the answer is 704 cu cm.
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Q14 HardSphere SA 616 sq cm (π = 22/7). Radius is:Explanation4πr² = 616, r² = 49, r = 7 cm. Hence the answer is 7 cm.
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DS1 Easy
What is the surface area of the sphere? (π = 22/7)
Statement IRadius is 7 cm.
Statement IIVolume is 1437 cu cm (approx.).
ExplanationStatement I alone: SA = 616 sq cm. Statement II alone gives approximate r but not exact SA without calculation. Answer: A. -
DS2 Easy
What is the radius of the sphere? (π = 22/7)
Statement ISurface area is 616 sq cm.
Statement IIVolume is 1437 cu cm (approx.).
ExplanationEach determines r = 7 cm. Answer: D.
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DS3 Easy
What is the total surface area of the hemisphere? (π = 22/7)
Statement IRadius is 7 cm.
Statement IICurved surface area is 308 sq cm.
ExplanationStatement I: TSA = 462 sq cm. Statement II: r = 7, TSA = 462 sq cm. Each alone sufficient. Answer: D. -
DS4 Medium
What is the volume of the hemisphere? (π = 22/7)
Statement IRadius is 7 cm.
Statement IICurved surface area is 308 sq cm.
ExplanationStatement I: V ≈ 718 cu cm. Statement II: r = 7 from CSA, same V. Each alone sufficient. Answer: D.