Mensuration
- Find the length of the longest rod that can be placed in a hall of 10 m length, 6 m breadth and 4 m height.
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The length of the longest rod = The diagonal of the hall
= √l² + b² + h²
= √10² + 6² + 4² = √100 + 36 + 16
= √152 = √2 × 2 × 38
= 2√38 mCorrect Option: A
The length of the longest rod = The diagonal of the hall
= √l² + b² + h²
= √10² + 6² + 4² = √100 + 36 + 16
= √152 = √2 × 2 × 38
= 2√38 m
- The volume of a cuboid is twice the volume of a cube. If the dimensions of the cuboid are 9 cm, 8 cm and 6 cm, the total surface area of the cube is :
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We have 2 × volume of cube = Volume of cuboid
⇒ 2 × (edge)³ = 9 × 8 × 6 cu.cm.
⇒ (edge)³ = 9 × 8 × 3
⇒ Edge = ³√3 × 3 × 3 × 2 × 2 × 2
= 3 × 2 = 6 cm.
∴ Total surface area of the cube = 6 × (edge)² = 6 × 6 × 6 = 216 cm².Correct Option: B
We have 2 × volume of cube = Volume of cuboid
⇒ 2 × (edge)³ = 9 × 8 × 6 cu.cm.
⇒ (edge)³ = 9 × 8 × 3
⇒ Edge = ³√3 × 3 × 3 × 2 × 2 × 2
= 3 × 2 = 6 cm.
∴ Total surface area of the cube = 6 × (edge)² = 6 × 6 × 6 = 216 cm².
- The length, breadth and height of a room is 5m, 4m and 3m respectively. Find the length of the largest bamboo that can be kept inside the room.
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Length of largest bamboo (Diagonal) = √(5)² + (4)² + (3)²
= √25 + 16 + 9 = √50
= √25 × 2 = 5√2mCorrect Option: D
Length of largest bamboo (Diagonal) = √(5)² + (4)² + (3)²
= √25 + 16 + 9 = √50
= √25 × 2 = 5√2m
- The length of the longest rod that can be placed in a room which is 12 m long, 9 m broad and 8 m high is
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The required length = Diagonal of the room
= √12² + 9² + 8² = √144 + 81 + 64
= √289 = 17mCorrect Option: C
The required length = Diagonal of the room
= √12² + 9² + 8² = √144 + 81 + 64
= √289 = 17m
- A cube of edge 5 cm is cut into cubes each of edge of 1 cm. The ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
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Surface area of a small cube = 6 × (edge)²
= 6 × 1 = 6 cm²
Surface area of the large cube = 6(5)² = 6 × 25 cm².∴ Required ratio = ; 6 = 1 or 1 : 25 6 × 25 25 Correct Option: D
Surface area of a small cube = 6 × (edge)²
= 6 × 1 = 6 cm²
Surface area of the large cube = 6(5)² = 6 × 25 cm².∴ Required ratio = ; 6 = 1 or 1 : 25 6 × 25 25
