381. A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total height of the toy is 10.2 cm, find the volume of the wooden toy (nearly).
     

1. 1. 104 cm³
      

   
   
   

   2. 162 cm³
      

   
   
   

   3. 427 cm³
      

   
   
   

   4. 266 cm³

   
   
   

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1. View Hint View Answer Discuss in Forum

   
   Radius of cone = 4.2cm
   Height of cone = 10.2 – 4.2 = 6cm
   Volume of the toy = Volume of cone + Volume of hemisphere
   

   =	1	π(4.2)² × 6 +	2	π (4.2)³
   	3		3

   
   

   =	1	π(4.2)²(6 + 2 × 4.2)
   	3

   
   

   =	1	×	22	× 4.2 × 4.2 × 14.4
   	3		7

   
   = 266 cu.cm.

   Correct Option: D

   
   Radius of cone = 4.2cm
   Height of cone = 10.2 – 4.2 = 6cm
   Volume of the toy = Volume of cone + Volume of hemisphere
   

   =	1	π(4.2)² × 6 +	2	π (4.2)³
   	3		3

   
   

   =	1	π(4.2)²(6 + 2 × 4.2)
   	3

   
   

   =	1	×	22	× 4.2 × 4.2 × 14.4
   	3		7

   
   = 266 cu.cm.

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382. The respective height and volume of a hemisphere and a right circular cylinder are equal, then the ratio of their radii is
     

1. 1. 2 : 3
      

   
   
   

   2. 3 : 1
      

   
   
   

   3. 3 : 2
      

   
   
   

   4. 2 : 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let Radius of hemisphere = Height of cylinder = r units
   

   ∴	Volume of hemisphere	= 1
   	Volume of cylinder

   
   

   ⇒	2	πr³h	= 1 ⇒		=
   	3			πr1²		3
   		r1²		r²		2

   
   

   ⇒	r	=	√3	or √3 : √2
   	r1		√2

   Correct Option: C

   Let Radius of hemisphere = Height of cylinder = r units
   

   ∴	Volume of hemisphere	= 1
   	Volume of cylinder

   
   

   ⇒	2	πr³h	= 1 ⇒		=
   	3			πr1²		3
   		r1²		r²		2

   
   

   ⇒	r	=	√3	or √3 : √2
   	r1		√2

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383. The ratio of the volume of a cube and of a solid sphere is 363 : 49. The ratio of an edge of the cube and the radius of the sphere is (taking π = 22/7 )
     

1. 1. 7 : 11
      

   
   
   

   2. 22 : 7
      

   
   
   

   3. 11 : 7
      

   
   
   

   4. 7: 22

   
   
   

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1. View Hint View Answer Discuss in Forum

   	Volume of the cube
   	Volume of the sphere

   
   

   	363
   	49

   
   

   =	x³		=	363
   		4		49
   		3

   
   

   ⇒	x³	=	363	×	4	×	22	=	121 × 4 × 22
   	r³		49		3		7		49 × 7

   
   

   ⇒	x³	=	11 × 11 × 11 × 2 × 2 × 2
   	r³		7 × 7 × 7

   
   \

   ∴	x	=	11 × 2	=	22	or 22 : 7
   	r		7		7

   Correct Option: B

   	Volume of the cube
   	Volume of the sphere

   
   

   	363
   	49

   
   

   =	x³		=	363
   		4		49
   		3

   
   

   ⇒	x³	=	363	×	4	×	22	=	121 × 4 × 22
   	r³		49		3		7		49 × 7

   
   

   ⇒	x³	=	11 × 11 × 11 × 2 × 2 × 2
   	r³		7 × 7 × 7

   
   \

   ∴	x	=	11 × 2	=	22	or 22 : 7
   	r		7		7

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384. From a right circular cylinder of radius 10 cm and height 21 cm, a right circular cone of same baseradius is removed. If the volume of the remaining portion is 4400 cm³, then the height of the removed cone (taking π = 22/7 ) is :
     

1. 1. 15 cm
      

   
   
   

   2. 18 cm
      

   
   
   

   3. 21 cm
      

   
   
   

   4. 24 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of the cylinder = πr²h
   = 22/7 × 10 × 10 × 21 = 6600 cu. cm
   Volume of the cone = 6600 – 4400 = 2200 cu.cm
   

   ∴ 2200 =	1	π × 10² × h
   	3

   
   

   ∴ 2200 =	2200	× h
   	21

   
   ⇒ h = 21 cm.

   Correct Option: C

   Volume of the cylinder = πr²h
   = 22/7 × 10 × 10 × 21 = 6600 cu. cm
   Volume of the cone = 6600 – 4400 = 2200 cu.cm
   

   ∴ 2200 =	1	π × 10² × h
   	3

   
   

   ∴ 2200 =	2200	× h
   	21

   
   ⇒ h = 21 cm.

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385. If a solid cone of volume 27π cm³ is kept inside a hollow cylinder whose radius and height are that of the cone, then the volume of water needed to fill the empty space is
     

1. 1. 3π cm³
      

   
   
   

   2. 18π cm³
      

   
   
   

   3. 54π cm³
      

   
   
   

   4. 8l π cm³

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of required water = 2 × volume of cone
   = 2 × 27π = 54π cu.cm

   Correct Option: C

   Volume of required water = 2 × volume of cone
   = 2 × 27π = 54π cu.cm

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