Practice Questions
Concept Explanation
Cube: all edges equal (a). Cuboid: rectangular box with length l, breadth w, height h.
Key Formulas
- Cube volume = a³ (cu cm or cu m)
- Cube surface area = 6a² (sq cm or sq m)
- Cuboid volume = l × w × h
- Cuboid surface area = 2(lw + wh + hl)
Example
Cube edge 5 cm: Volume = 125 cu cm, SA = 150 sq cm.
Common Trap
Volume is in cubic units; surface area is in square units.
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Q1 Easy
Volume of a cube of edge 5 cm is:
ExplanationVolume = 5³ = 125 cu cm. -
Q2 Easy
Surface area of a cube of edge 5 cm is:
ExplanationSA = 6 × 25 = 150 sq cm. -
Q3 Easy
Volume of a cuboid 4 cm × 3 cm × 2 cm is:
ExplanationVolume = 4 × 3 × 2 = 24 cu cm. -
Q4 Medium
Surface area of cuboid 4 cm × 3 cm × 2 cm is:
ExplanationSA = 2(12 + 6 + 8) = 52 sq cm. -
Q5 Easy
Edge of a cube is 6 cm. Total surface area is:
ExplanationSA = 6 × 36 = 216 sq cm. -
Q6 Medium
A cube has volume 64 cu cm. Edge length is:
Explanationa³ = 64, so a = 4 cm. -
Q7 Easy
Cuboid dimensions 10 cm × 6 cm × 4 cm. Volume is:
ExplanationVolume = 240 cu cm.
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Q8 Medium
Cuboid 10 cm × 6 cm × 4 cm. Surface area is:
ExplanationSA = 2(60 + 24 + 40) = 248 sq cm. -
Q9 Medium
A cube edge is 8 cm. Volume is:
ExplanationVolume = 8³ = 512 cu cm. -
Q10 Hard
Sum of lengths of all edges of a cube of side 7 cm is:
ExplanationA cube has 12 edges: 12 × 7 = 84 cm. -
Q11 Medium
A cuboidal tank 2 m × 1.5 m × 1 m holds water in cu m:
ExplanationVolume = 2 × 1.5 × 1 = 3 cu m. -
Q12 Hard
Cost of painting all faces of a cube (edge 2 m) at Rs. 50 per sq m is:
ExplanationSA = 6 × 4 = 24 sq m. Cost = 24 × 50 = Rs. 1200. -
Q13 Hard
Cube volume 125 cu cm. Surface area is:
ExplanationEdge = 5 cm. SA = 150 sq cm. -
Q14 Hard
A cuboid has volume 360 cu cm, length 10 cm, breadth 6 cm. Height is:
ExplanationHeight = 360/(10 × 6) = 6 cm.
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DS1 Easy
What is the volume of the cube?
Statement IEdge is 6 cm.
Statement IISurface area is 216 sq cm.
ExplanationEach alone gives edge 6 cm and volume 216 cu cm. -
DS2 Medium
What is the surface area of the cuboid?
Statement ILength 8 cm, breadth 5 cm, height 3 cm.
Statement IIVolume is 120 cu cm.
ExplanationStatement I alone gives SA = 158 sq cm. Volume alone does not fix dimensions.
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DS3 Easy
What is the edge of the cube?
Statement IVolume is 27 cu cm.
Statement IITotal surface area is 54 sq cm.
ExplanationEach alone gives edge = 3 cm. -
DS4 Easy
What is the volume of the cuboid?
Statement ILength is 12 cm and breadth is 5 cm.
Statement IIHeight is 4 cm.
ExplanationNeed both with one dimension pair: volume = 240 cu cm.