Mensuration
- A cylindrical pencil of diameter 1.2 cm has one of its ends sharpened into a conical shape of height 1.4 cm. The volume of the material removed is
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Volume of removed material = πr²h - 1 πr²h = 2 πr²h 3 3 = 
2 × 22 × 0.6 × 0.6 × 1.4 
cu.cm. 3 7
= 1.056 cu. cm.Correct Option: A
Volume of removed material = πr²h - 1 πr²h = 2 πr²h 3 3 = 2 × 22 × 0.6 × 0.6 × 1.4 cu.cm. 3 7
= 1.056 cu. cm.
- The diameters of the internal and external surfaces of a hollow spherical shell are 6 cm and 10 cm respectively. If it is melted and a solid cylinder of length 8/3 cm is made, then the diameter (in cm) of the cylinder is
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Volume of the material of the hollow cylinder
= 4 π(R² - r²) 3 = 4 π(5² - 3²) 3 = 4 π(125 - 27) 3 = 4 × 98 π cu.cm. 3
If the radius of the cylinder be R cm, thenπR² × 8 = 4 × 98π 3 3 ⇒ R² = 4 × 98 = 49 8
⇒ R = √49 = 7 cm.
∴ Diameter = 2R = 2 × 7 = 14 cm.Correct Option: B
Volume of the material of the hollow cylinder
= 4 π(R² - r²) 3 = 4 π(5² - 3²) 3 = 4 π(125 - 27) 3 = 4 × 98 π cu.cm. 3
If the radius of the cylinder be R cm, thenπR² × 8 = 4 × 98π 3 3 ⇒ R² = 4 × 98 = 49 8
⇒ R = √49 = 7 cm.
∴ Diameter = 2R = 2 × 7 = 14 cm.
- The volume of a metallic cylindrical pipe is 748 cm3. Its length is 14 cm and external radius is 9 cm. Its thickness is
(Use π = 22/7 )
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According to the question, π(R² – r²) h = 748
⇒ 22 (R² – r²) × 14 = 748 7 ⇒ R² – r² = 748 × 7 = 17 22 × 14
⇒ 9² – r² = 17
⇒ 81 – r² = 17
⇒ r² = 81 – 17 = 64
⇒ r = 64 = 8 cm.
∴ Thickness of pipe = R – r = 9 – 8 = 1 cm.Correct Option: A
According to the question, π(R² – r²) h = 748
⇒ 22 (R² – r²) × 14 = 748 7 ⇒ R² – r² = 748 × 7 = 17 22 × 14
⇒ 9² – r² = 17
⇒ 81 – r² = 17
⇒ r² = 81 – 17 = 64
⇒ r = 64 = 8 cm.
∴ Thickness of pipe = R – r = 9 – 8 = 1 cm.
- A cylindrical vessel of diameter 24 cm contains some water. If two spheres of radii 6 cm each are lowered into the water until they are completely immersed, then the water level (in cm) in the vessel will rise by
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Volume of the two spheres of radius 6 cm. each
= 2 × 4 πr³ 3 = 2 × 4 π(6)³ 3
= 576 p cu. cm.
According to the question, π × 12 × 12 × h = 576π⇒ h = 576 = 4 cm. 12 × 12 Correct Option: C
Volume of the two spheres of radius 6 cm. each
= 2 × 4 πr³ 3 = 2 × 4 π(6)³ 3
= 576 p cu. cm.
According to the question, π × 12 × 12 × h = 576π⇒ h = 576 = 4 cm. 12 × 12
- The perimeter of one face of a cube is 20 cm. Its volume will be
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Perimeter of a face of cube = 20 cm.
∴ An edge of cube = 20 = 5 cm. 4
∴ Volume of cube = (edge)³ = (5)³ = 125 cu. cm.Correct Option: C
Perimeter of a face of cube = 20 cm.
∴ An edge of cube = 20 = 5 cm. 4
∴ Volume of cube = (edge)³ = (5)³ = 125 cu. cm.
