Mensuration
- If diagonal of a cube is √12 cm, then its volume in cubic cm is:
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Diagonal of cube = √3a²
∴ According to question,
√3a = 2√3
∴ Its volume = a³ = 2³ = 8cu cmCorrect Option: A
Diagonal of cube = √3a²
∴ According to question,
√3a = 2√3
∴ Its volume = a³ = 2³ = 8cu cm
- If the volume of two cubes are in the ratio 27 : 1, the ratio of their edge is :
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Volume of cube = (Side)³
∴ Ratio of volume = 27 : 1∴ Ratio of the edges = 3√ 27 1
or 3 : 1Correct Option: A
Volume of cube = (Side)³
∴ Ratio of volume = 27 : 1∴ Ratio of the edges = 3√ 27 1
or 3 : 1
- The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88cm². The volume of the cuboid is :
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Surface area of cuboid = 2 × (l × b + b × h + h × l)
= 2 (3x × 2x + 2x × x + x × 3x)
= 2 (6x² + 2x² + 3x²) = 22x²
∴ 22x² = 88
⇒ x²= 4 ⇒
⇒ X = √4 = 2
∴ l = 6 cm, b = 4 cm, h = 2 cm
∴ Volume of cuboid = l × b × h = 6 × 4 × 2 cm³ = 48 cm³Correct Option: C
Surface area of cuboid = 2 × (l × b + b × h + h × l)
= 2 (3x × 2x + 2x × x + x × 3x)
= 2 (6x² + 2x² + 3x²) = 22x²
∴ 22x² = 88
⇒ x²= 4 ⇒
⇒ X = √4 = 2
∴ l = 6 cm, b = 4 cm, h = 2 cm
∴ Volume of cuboid = l × b × h = 6 × 4 × 2 cm³ = 48 cm³
- If the ratio of the diameters of two right circular cones of equal height be 3 : 4, then the ratio of their volume will be
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Ratio of the volumes of cone = 1 πr1²h 3 = 
r1 
² = 3 ² × 9 or 9 : 16 1 πr²h r2 4 16 3 Correct Option: B
Ratio of the volumes of cone = 1 πr1²h 3 = r1 ² = 3 ² × 9 or 9 : 16 1 πr²h r2 4 16 3
- A cuboidal water tank has 216 litres of water. Its depth is 1/3 of its length and breadth is 1/2 of 1/3 of the difference of length and breadth. The length of the tankis
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Let the length of tank = x dm
Depth = x dm 3 ⇒ Breadth = x - x × 1 × 1 3 3 2 = 2x × 1 × 1 = x dm 3 3 2 9 ∴ Volume of tank = x × x × x = x³ 9 3 27
According to the question,x³ = 216 27
⇒ x³ = 27 × 216
⇒ x = (27 × 216)1/3
∴ x = 3 × 6 = 18 dmCorrect Option: B
Let the length of tank = x dm
Depth = x dm 3 ⇒ Breadth = x - x × 1 × 1 3 3 2 = 2x × 1 × 1 = x dm 3 3 2 9 ∴ Volume of tank = x × x × x = x³ 9 3 27
According to the question,x³ = 216 27
⇒ x³ = 27 × 216
⇒ x = (27 × 216)1/3
∴ x = 3 × 6 = 18 dm
