Practice Questions
Concept Explanation
Volume measures space occupied (cu cm, cu m). Surface area measures total outer area (sq cm, sq m).
Summary Table
- Cube: V = a³, SA = 6a²
- Cuboid: V = lwh, SA = 2(lw + wh + 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 = 1 cu dm.
Example
Cylinder r = 7 cm, h = 10 cm: V = 1540 cu cm = 1.54 L.
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Q1 Easy
Cube edge 4 cm. Volume and total surface area are:
ExplanationV = 64 cu cm, SA = 6 × 16 = 96 sq cm. -
Q2 Easy
Cuboid 5 cm × 4 cm × 3 cm. Volume is:
ExplanationV = 60 cu cm. -
Q3 Medium
Cylinder 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. -
Q4 Medium
Cone and cylinder share r = 7 cm, h = 12 cm (π = 22/7). Combined volume is:
ExplanationCylinder 1848 + cone 616 = 2464 cu cm. -
Q5 Hard
Cylinder r = 7 cm, h = 3 cm and cone with same r have equal volume (π = 22/7). Cone height is:
ExplanationCylinder V = 462 cu cm. Cone h = 462 × 3 / (22/7 × 49) = 9 cm. -
Q6 Medium
Cuboid 5 cm × 4 cm × 3 cm. Total surface area is:
ExplanationSA = 2(20 + 12 + 15) = 94 sq cm. -
Q7 Medium
A tank 2 m × 1.5 m × 1 m is filled with water. Capacity in litres is:
ExplanationVolume = 3 cu m = 3 000 000 cu cm = 3000 L.
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Q8 Medium
Cube volume 216 cu cm. Total surface area is:
ExplanationEdge = 6 cm. SA = 6 × 36 = 216 sq cm. -
Q9 Hard
Cylinder CSA 440 sq cm, height 10 cm, π = 22/7. TSA is:
Explanationr = 7 cm from CSA. TSA = 748 sq cm. -
Q10 Hard
Sphere and cube have equal surface area. Sphere r = 7 cm, π = 22/7. Cube edge is approximately:
ExplanationSphere SA = 616. Cube 6a² = 616, a = √(102.67) ≈ 10.1 cm. -
Q11 Easy
1 cu m equals how many cu cm?
Explanation1 m = 100 cm, so 1 cu m = 100³ = 1 000 000 cu cm. -
Q12 Hard
A cone of height 12 cm is filled with water up to half its height. Fraction of full volume filled is:
ExplanationSimilar cones: linear ratio 1/2 gives volume ratio (1/2)³ = 1/8. -
Q13 Hard
Cost of painting cuboid box 10 cm × 8 cm × 6 cm at Rs. 5 per sq cm is:
ExplanationSA = 376 sq cm. Cost = 376 × 5 = Rs. 1880. -
Q14 Medium
Open-top cubical box of edge 5 cm. Area to be painted (inside and outside, five faces each) is:
ExplanationFive faces inside and five outside: 10 × 25 = 250 sq 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: volume = 240 cu cm. -
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.
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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 alone gives volume ≈ 1437 cu cm. -
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.