Mensuration
- The height of a circular cylinder is increased six times and the base area is decreased to oneninth of its value. The factor by which the lateral surface of the cylinder increases is
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Curved surface of cylinder = 2πrh Now,
Radius = 2π × 1 r ; height = 6h 3 Curved surface = 1 r × 6h = (2πrh) × 2 3
∴ Increase will be twice.Correct Option: A
Curved surface of cylinder = 2πrh Now,
Radius = 2π × 1 r ; height = 6h 3 Curved surface = 1 r × 6h = (2πrh) × 2 3
∴ Increase will be twice.
- The radius and height of a cylinder are in the ratio. 5 : 7 and its volume is 550 cm3. Calculate its curved surface area in sq. cm.
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V = πr²h
⇒ 550 = π × 5x × 5x × 7x⇒ 550 = 22 × 25 × 7³ 7 ⇒ x³ = 550 = 1 ⇒ x = 1 22 × 25
V = πr²h∴ Area of curved surface = 2 × 22 × 5 × 7 = 220 sq.cm. 7
⇒ 550 = π × 5x × 5x × 7x⇒ 550 = 22 × 25 × 7³ 7 ⇒ x³ = 550 = 1 ⇒ x = 1 22 × 25 ∴ Area of curved surface = 2 × 22 × 5 × 7 = 220 sq.cm. 7 Correct Option: C
V = πr²h
⇒ 550 = π × 5x × 5x × 7x⇒ 550 = 22 × 25 × 7³ 7 ⇒ x³ = 550 = 1 ⇒ x = 1 22 × 25 ∴ Area of curved surface = 2 × 22 × 5 × 7 = 220 sq.cm. 7
- The area of the curved surface and the area of the base of a right circular cylinder are a square cm and b square cm respectively. The height of the cylinder is
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Curved surface of cylinder = 2πrh = a
Area of base = πr² = b
∴ 2πrh = a
⇒ 4π²r²h² = a² ⇒ 4πbh² = a²⇒ h² = a² 4πb ⇒ h = a cm. 2√πb Correct Option: C
Curved surface of cylinder = 2πrh = a
Area of base = πr² = b
∴ 2πrh = a
⇒ 4π²r²h² = a² ⇒ 4πbh² = a²⇒ h² = a² 4πb ⇒ h = a cm. 2√πb
- Find the length of the largest rod that can be placed in a room 16m long, 12m broad and 10(2/3) m. high.
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Length of the largest rod = √l² + b² + h²
= √16² + 12² + 
32 
² 3 = √ 400 + 1024 = √ 4624 = 68 = 22 2 m 9 9 3 3 Correct Option: C
Length of the largest rod = √l² + b² + h²
= √16² + 12² + 32 ² 3 = √ 400 + 1024 = √ 4624 = 68 = 22 2 m 9 9 3 3
- If the volume and surface area of a sphere are numerically the same, then its radius is :
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Let the radius of the sphere be r units.
According to the question,4 πr³ = 4πr² ⇒ r = 3 units 3 Correct Option: C
Let the radius of the sphere be r units.
According to the question,4 πr³ = 4πr² ⇒ r = 3 units 3
