186. The radii of the base of two cylinders are in the ratio 3 : 5 and their heights in the ratio 2 : 3. The ratio of their curved surface will be :
     

1. 1. 2 : 5
      

   
   
   

   2. 2 : 3
      

   
   
   

   3. 3 : 5
      

   
   
   

   4. 5 : 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let for the first cylinder,
   r₁ = 3x
   h₁ = 2y For the second cylinder,
   r₂ = 5x
   h₂ = 3y
   

   ∴	2πr1h1	=	2π × 3x × 2y	=	2
   	2πr2h2		2π × 5x × 3y		5

   
   ⇒ 2 : 5

   Correct Option: A

   Let for the first cylinder,
   r₁ = 3x
   h₁ = 2y For the second cylinder,
   r₂ = 5x
   h₂ = 3y
   

   ∴	2πr1h1	=	2π × 3x × 2y	=	2
   	2πr2h2		2π × 5x × 3y		5

   
   ⇒ 2 : 5

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187. Water flows through a cylindrical pipe, whose radius is 7 cm, at 5 metre per second. The time, it takes to fill an empty water tank, with height 1.54 metres and area of the base (3 × 5) square metres, is (take π = 22/7)
     

1. 1. 6 minutes
      

   
   
   

   2. 5 minutes
      

   
   
   

   3. 10 minutes
      

   
   
   

   4. 9 minutes

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of the tank = (3 × 5 × 1.54) cu.metre
   Volume of water flowing through pipe per second
   

   = π ×		7		²	× 5 m³
   		100

   
   

   ∴ Required time =	3 × 5 × 1.54 × 100 × 100 × 7	= 300 second = 5 minutes
   	22 × 7 × 7 × 5

   Correct Option: B

   Volume of the tank = (3 × 5 × 1.54) cu.metre
   Volume of water flowing through pipe per second
   

   = π ×		7		²	× 5 m³
   		100

   
   

   ∴ Required time =	3 × 5 × 1.54 × 100 × 100 × 7	= 300 second = 5 minutes
   	22 × 7 × 7 × 5

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188. A solid cylinder has total surface area of 462 sq.cm. Its curved
     surface area is 1/3rd of the total surface area. Then the radius of the cylinder is
     

1. 1. 7 cm
      

   
   
   

   2. 3.5 cm
      

   
   
   

   3. 9 cm
      

   
   
   

   4. 11 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Area of the curved surface =	1	× 462 = 154 sq.cm.
   	3

   
   ∴ 2πrh + 2πr² = 462
   ⇒ 154 + 2πr² = 462
   ⇒ 2πr² = 462 – 154 = 308
   

   ⇒ r² =	308	=	308 × 7	= 49
   	2π		2 × 22

   
   ⇒ r = √49 = 7 cm

   Correct Option: A

   Area of the curved surface =	1	× 462 = 154 sq.cm.
   	3

   
   ∴ 2πrh + 2πr² = 462
   ⇒ 154 + 2πr² = 462
   ⇒ 2πr² = 462 – 154 = 308
   

   ⇒ r² =	308	=	308 × 7	= 49
   	2π		2 × 22

   
   ⇒ r = √49 = 7 cm

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189. The diameter of a cylinder is 7 cm and its height is 16 cm. Using the value of π = 22/7 , the lateral surface area of the cylinderis
     

1. 1. 352 cm.²
      

   
   
   

   2. 350 cm.²
      

   
   
   

   3. 355 cm.²
      

   
   
   

   4. 348 cm.²

   
   
   

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1. View Hint View Answer Discuss in Forum

   Lateral surface area of the cylinder = 2πrh
   

   = 2 ×	22	×	7	× 16 = 352 sq.cm
   	7		2

   Correct Option: A

   Lateral surface area of the cylinder = 2πrh
   

   = 2 ×	22	×	7	× 16 = 352 sq.cm
   	7		2

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190. The height of a solid right circular cylinder is 6 metres and three times the sum of the area of its two end faces is twice the area of its curved surface. The radius of its base (in metre) is
     

1. 1. 4
      

   
   
   

   2. 2
      

   
   
   

   3. 8
      

   
   
   

   4. 10

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the radius of the base be r metre.
   then 3 × 2πr² = 2 × 2πrh
   ⇒ 3r = 2h
   ⇒ 3r = 2 × 6
   ⇒ r = 4 metre

   Correct Option: A

   Let the radius of the base be r metre.
   then 3 × 2πr² = 2 × 2πrh
   ⇒ 3r = 2h
   ⇒ 3r = 2 × 6
   ⇒ r = 4 metre

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