Practice Questions
Concept Explanation
Cube: all edges equal a. Cuboid: length l, breadth b, height h.
Formulas
- Cube volume V = a³; total surface area TSA = 6a²
- Cuboid V = lbh; TSA = 2(lb + bh + hl)
- Space diagonal of cuboid = √(l² + b² + h²)
- Cube diagonal = a√3
Example
Cube edge 4 cm: V = 64 cu cm, TSA = 96 sq cm.
Common Trap
Lateral surface area excludes top and bottom; total surface area includes all faces.
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Q1 EasyVolume of a cube of edge 5 cm is:ExplanationV = 5³ = 125 cu cm. Hence the answer is 125 cu cm.
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Q2 EasyCuboid volume 360 cu cm, base 12 × 5 cm. Height:Explanationh = 360 / 60 = 6 cm. Hence the answer is 6 cm.
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Q3 EasyTotal surface area of cube edge 4 cm is:ExplanationTSA = 6 × 4² = 96 sq cm. Hence the answer is 96 sq cm.
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Q4 EasyCuboid 10 cm × 6 cm × 4 cm. Volume is:ExplanationV = 10 × 6 × 4 = 240 cu cm. Hence the answer is 240 cu cm.
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Q5 EasyCuboid 8 × 5 × 2 cm. Volume:Explanation8 × 5 × 2 = 80 cu cm. Hence the answer is 80 cu cm.
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Q6 EasyCube volume 216 cu cm. Edge is:Explanationa³ = 216, a = 6 cm. Hence the answer is 6 cm.
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Q7 MediumCube TSA 150 sq cm. Edge is:Explanation6a² = 150, a = 5 cm. Hence the answer is 5 cm.
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Q8 MediumCube edge doubled. Volume becomes:ExplanationNew volume = (2a)³ = 8a³. Hence the answer is 8 times.
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Q9 MediumOpen-top cubical box edge 5 cm. Area of five faces:Explanation5 × 25 = 125 sq cm. Hence the answer is 125 sq cm.
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Q10 MediumCuboid 10 × 6 × 4 cm. Total surface area is:ExplanationTSA = 2(60 + 24 + 40) = 248 sq cm. Hence the answer is 248 sq cm.
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Q11 MediumCube edge 3 cm. Lateral surface area (four faces):ExplanationLSA = 4 × 9 = 36 sq cm. Hence the answer is 36 sq cm.
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Q12 HardCuboid length 12 cm, breadth 4 cm, height 3 cm. Space diagonal:ExplanationDiagonal = √(144 + 16 + 9) = √169 = 13 cm. Hence the answer is 13 cm.
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Q13 HardCube surface area 54 sq cm. Volume:Explanation6a² = 54, a = 3, V = 27 cu cm. Hence the answer is 27 cu cm.
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Q14 HardCube diagonal length if edge is 6 cm is:ExplanationSpace diagonal = a√3 = 6√3 cm. Hence the answer is 6√3 cm.
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DS1 Easy
What is the volume of the cube?
Statement ITotal surface area is 150 sq cm.
Statement IIEdge is 5 cm.
ExplanationStatement I: a = 5, V = 125 cu cm. Statement II: V = 125 cu cm. Each alone sufficient. Answer: D. -
DS2 Easy
What is the edge of the cube?
Statement IVolume is 512 cu cm.
Statement IITotal surface area is 384 sq cm.
ExplanationEach gives a = 8 cm. Answer: D.
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DS3 Easy
What is the volume of the cuboid?
Statement ILength 12 cm, breadth 5 cm, height 6 cm.
Statement IIBase area 60 sq cm and height 6 cm.
ExplanationEach gives V = 360 cu cm. Answer: D. -
DS4 Medium
What is the total surface area of the cuboid?
Statement IDimensions are 10 cm, 6 cm and 4 cm.
Statement IIVolume is 240 cu cm and base area is 60 sq cm.
ExplanationStatement I alone: TSA = 248 sq cm. Statement II alone: height = 4 but length and breadth not fixed uniquely. Answer: A.