Practice Questions
Concept Explanation
Volume measures space occupied (cu units). Surface area measures total outer area (sq units). Use π = 22/7 for circular solids in placement numerics.
Summary Table
- Cube: V = a³, TSA = 6a²
- Cuboid: V = lbh, TSA = 2(lb + bh + hl)
- Cylinder: V = πr²h, TSA = 2πr(r + h)
- Cone: V = (1/3)πr²h, TSA = πr(r + l)
- Sphere: V = (4/3)πr³, SA = 4πr²
Conversion
1 cu m = 1 000 000 cu cm. 1 L = 1000 cu cm.
Common Trap
Mixing units (cm vs m) and using diameter where radius is required.
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Q1 EasyCube edge 4 cm. Volume and total surface area are:ExplanationV = 64 cu cm, TSA = 6 × 16 = 96 sq cm. Hence the answer is 64 cu cm, 96 sq cm.
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Q2 EasyCuboid 5 cm × 4 cm × 3 cm. Volume is:ExplanationV = 60 cu cm. Hence the answer is 60 cu cm.
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Q3 Easy1 cu m equals how many cu cm?Explanation100³ = 1 000 000. Hence the answer is 1 000 000.
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Q4 MediumCuboid 5 × 4 × 3 cm. Total surface area:ExplanationTSA = 2(20 + 12 + 15) = 94 sq cm. Hence the answer is 94 sq cm.
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Q5 MediumTank 2 m × 1.5 m × 1 m. Capacity in litres:ExplanationV = 3 cu m = 3 000 000 cu cm = 3000 L. Hence the answer is 3000 L.
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Q6 MediumCube volume 216 cu cm. Total surface area:ExplanationEdge = 6 cm, TSA = 216 sq cm. Hence the answer is 216 sq cm.
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Q7 MediumCylinder r = 7 cm, h = 10 cm (π = 22/7). Volume in litres (1000 cu cm = 1 L) is:ExplanationV = 1540 cu cm = 1.54 L. Hence the answer is 1.54 L.
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Q8 MediumCone and cylinder share r = 7 cm, h = 12 cm (π = 22/7). Combined volume is:ExplanationCylinder 1848 + cone 616 = 2464 cu cm. Hence the answer is 2464 cu cm.
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Q9 MediumOpen-top cubical box edge 5 cm. Area to paint (inside and outside, five faces each):Explanation10 faces × 25 = 250 sq cm. Hence the answer is 250 sq cm.
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Q10 HardCylinder CSA 440 sq cm, height 10 cm (π = 22/7). TSA:Explanationr = 7 cm, TSA = 748 sq cm. Hence the answer is 748 sq cm.
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Q11 HardCone height 12 cm filled to half height. Fraction of full volume:ExplanationSimilar solids: (1/2)³ = 1/8. Hence the answer is 1/8.
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Q12 HardCylinder r = 7 cm, h = 3 cm and cone with same r have equal volume (π = 22/7). Cone height is:ExplanationCylinder V = 462. Cone h = 462 × 3 / 154 = 9 cm. Hence the answer is 9 cm.
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Q13 HardCost of painting cuboid box 10 cm × 8 cm × 6 cm at Rs. 5 per sq cm is:ExplanationTSA = 376 sq cm. Cost = 376 × 5 = Rs. 1880. Hence the answer is Rs. 1880.
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Q14 HardSphere r = 7 cm and cube edge 10 cm (π = 22/7). Difference of volumes (sphere minus cube) nearest:ExplanationSphere ≈ 1437, cube = 1000, difference ≈ 437 cu cm. Hence the answer is 437 cu cm.
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DS1 Easy
What is the volume of the cuboid?
Statement ILength 10 cm, breadth 6 cm, height 4 cm.
Statement IITotal surface area is 248 sq cm.
ExplanationStatement I alone: V = 240 cu cm. Statement II alone does not fix dimensions uniquely. Answer: A. -
DS2 Easy
What is the total surface area of the cylinder? (π = 22/7)
Statement IRadius is 7 cm.
Statement IIHeight is 10 cm.
ExplanationNeed both: TSA = 748 sq cm. Answer: C.
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DS3 Medium
What is the volume of the sphere? (π = 22/7)
Statement IRadius is 7 cm.
Statement IISurface area is 616 sq cm.
ExplanationEach gives r = 7, V ≈ 1437 cu cm. Answer: D. -
DS4 Hard
What is the combined volume of cylinder and cone with same r and h? (π = 22/7)
Statement Ir = 7 cm and h = 12 cm.
Statement IICylinder volume is 1848 cu cm and cone volume is one-third of it.
ExplanationStatement I alone: 1848 + 616 = 2464 cu cm. Statement II describes relation but needs base volume. Answer: A.