Mensuration
- A right circular cylinder of height 16 cm is covered by a rectangular tin foil of size 16 cm × 22 cm. The volume of the cylinder is
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Curved surface area of cylinder = Area of rectangular tin foil
⇒ 2πrh = 16 × 22= 2 × 22 × r × 16 = 16 × 22 7 ⇒ r = 7 cm 2
∴ Volume of the cylinder = πr&suph;= 22 × 7 × 7 × 16 = 616 cm³ 7 2 2 Correct Option: C
Curved surface area of cylinder = Area of rectangular tin foil
⇒ 2πrh = 16 × 22= 2 × 22 × r × 16 = 16 × 22 7 ⇒ r = 7 cm 2
∴ Volume of the cylinder = πr&suph;= 22 × 7 × 7 × 16 = 616 cm³ 7 2 2
- Two iron sheets each of diameter 6 cm are immersed in the water contained in a cylindrical vessel of radius 6 cm. The level of the water in the vessel will be raised by
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When the two iron sheets are immersed in water, it will displace water equal to its volume. Let the water be raised in the vessel by x cm.
= 2 × 4 × π × (3)³ = π × (6)² × x 3
⇒ 72π = 36 px⇒ x = 72 = 2 cm 36 Correct Option: B
When the two iron sheets are immersed in water, it will displace water equal to its volume. Let the water be raised in the vessel by x cm.
= 2 × 4 × π × (3)³ = π × (6)² × x 3
⇒ 72π = 36 px⇒ x = 72 = 2 cm 36
- Water is being pumped out through a circular pipe whose internal diameter is 7cm. If the flow of water is 12 cm per second, how many litres of water is being pumped out in one hour ?
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Volume of water flowing per second = πr²h
= 22 × 7 × 7 × 12 = 462 cm³ 7 2 2
∴ Volume of water pumped out in 1 hour = 462 × 60 × 60 cm³
= 1663200 cm³ = 1663.2 litresCorrect Option: A
Volume of water flowing per second = πr²h
= 22 × 7 × 7 × 12 = 462 cm³ 7 2 2
∴ Volume of water pumped out in 1 hour = 462 × 60 × 60 cm³
= 1663200 cm³ = 1663.2 litres
- The lateral surface area of a cylinder is 1056 cm² and its height is 16cm. Find its volume.
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Let the radius of base be r cm and height be 16 cm. then 2πrh = 1056
= 2 × 22 × r × 16 = 1056 7 ⇒ r = 1056 × 7 = 21 cm. 2 × 22 × 16 2
∴ Volume of the cylinder = πr²h= 22 × 21 × 21 × 16 = 5544 cm³ 7 2 2 Correct Option: D
Let the radius of base be r cm and height be 16 cm. then 2πrh = 1056
= 2 × 22 × r × 16 = 1056 7 ⇒ r = 1056 × 7 = 21 cm. 2 × 22 × 16 2
∴ Volume of the cylinder = πr²h= 22 × 21 × 21 × 16 = 5544 cm³ 7 2 2
- A cylinder has 'r' as the radius of the base and 'h' as the height. The radius of base of another cylinder, having double the volume but the same height as that of the first cylinder must be equal to
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Let the radius of the new cylinder be R then,
2πr²h = πR²h
⇒ R² = 2r² ⇒ R = √2r = r√2Correct Option: C
Let the radius of the new cylinder be R then,
2πr²h = πR²h
⇒ R² = 2r² ⇒ R = √2r = r√2
