376. A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their respective volume is
     

1. 1. 1 : 2 : 3
      

   
   
   

   2. 2 : 1 : 3
      

   
   
   

   3. 1 : 3 : 2
      

   
   
   

   4. 3 : 1 : 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Required ratio =	1	πr²h :	2	πr²h : πr²h
   	3		3

   
   

   =	1	:	2	: 1 : 2 : 3
   	3		3

   Correct Option: A

   Required ratio =	1	πr²h :	2	πr²h : πr²h
   	3		3

   
   

   =	1	:	2	: 1 : 2 : 3
   	3		3

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377. A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their respective volume is
     

1. 1. 1 : 2 : 3
      

   
   
   

   2. 2 : 1 : 3
      

   
   
   

   3. 1 : 3 : 2
      

   
   
   

   4. 3 : 1 : 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Required ratio =	1	πr²h :	2	πr²h : πr²h
   	3		3

   
   

   =	1	:	2	: 1 : 2 : 3
   	3		3

   Correct Option: A

   Required ratio =	1	πr²h :	2	πr²h : πr²h
   	3		3

   
   

   =	1	:	2	: 1 : 2 : 3
   	3		3

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378. The height of a cylinder and that of a cone are in the ratio 2 : 3 and the radii of their bases in the ratio 3 : 4. The ratio of their volume will be
     

1. 1. 1 : 9
      

   
   
   

   2. 2 : 9
      

   
   
   

   3. 9 : 8
      

   
   
   

   4. 3 : 8

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let radius of cylinder = 3x
   radius of cone = 4x
   Also, let height of cylinder = 2y and height of cylinder = 3y
   

   	Volume of the cylinder
   	Volumeof the cone

   
   

   =
   	π	(3x)² × 2y		=	18πx²y	= 9 : 8
   	1	π(4x)² × 3y			16πx²y
   	3

   Correct Option: C

   Let radius of cylinder = 3x
   radius of cone = 4x
   Also, let height of cylinder = 2y and height of cylinder = 3y
   

   	Volume of the cylinder
   	Volumeof the cone

   
   

   =
   	π	(3x)² × 2y		=	18πx²y	= 9 : 8
   	1	π(4x)² × 3y			16πx²y
   	3

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379. A conical vessel whose internal radius is 12 cm and height 50 cm is full of liquid. The contents are emptied into a cylindrical vessel with radius (internal) 10 cm. The height to which the liquid rises in the cylindrical vessel is :
     

1. 1. 25cm
      

   
   
   

   2. 20cm
      

   
   
   

   3. 24cm
      

   
   
   

   4. 22cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   In both the vessels, the volume of liquid will be same.
   ∴ Volume of liquid in cylinder = Volume of liquid in cone.
   Let the height of liquid column in cylinder be h cm, then
   

   πr²h =	1	π × (12)² × 50
   	3

   
   

   ∴ h =	1	×	12 × 12 × 50
   	3		10 × 10

   
   = 24cm

   Correct Option: C

   In both the vessels, the volume of liquid will be same.
   ∴ Volume of liquid in cylinder = Volume of liquid in cone.
   Let the height of liquid column in cylinder be h cm, then
   

   πr²h =	1	π × (12)² × 50
   	3

   
   

   ∴ h =	1	×	12 × 12 × 50
   	3		10 × 10

   
   = 24cm

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380. The total surface area of a solid right circular cylinder is twice that of a solid sphere. If they have the same radii, the ratio of the volume of the cylinder to that of the sphere is given by
     

1. 1. 9 : 4
      

   
   
   

   2. 2 : 1
      

   
   
   

   3. 3 : 1
      

   
   
   

   4. 4 : 9

   
   
   

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1. View Hint View Answer Discuss in Forum

   According to question, 2πrh + 2πr² = 8πr²
   ⇒ 2πrh = 6πr²
   

   ∴ Required time =	154	= 2 hours
   	r

   
   

   ∴ Required ratio = πr²h :	4	πr³
   	3

   
   = 3h : 4r = 9 : 4

   Correct Option: A

   According to question, 2πrh + 2πr² = 8πr²
   ⇒ 2πrh = 6πr²
   

   ∴ Required time =	154	= 2 hours
   	r

   
   

   ∴ Required ratio = πr²h :	4	πr³
   	3

   
   = 3h : 4r = 9 : 4

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