396. The surface areas of two spheres are in the ratio 4 : 9. Their volumes will be in the ratio
     

1. 1. 2 : 3
      

   
   
   

   2. 4 :9
      

   
   
   

   3. 8 : 27
      

   
   
   

   4. 64 : 729

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the radii of the first and second sphere be r₁ and r₂ units respectively.
   According to the question,
   

   	4πr1²	=	4
   	4πr2²		9

   
   

   ∴

   =

   4

   πr1³

   V1

   3

   =

   r1

   ³

   =

   2

   ³

   ×

   8

   or 8 : 27

   V2

   4

   πr2³

   r2

   3

   27

   3

   Correct Option: C

   Let the radii of the first and second sphere be r₁ and r₂ units respectively.
   According to the question,
   

   	4πr1²	=	4
   	4πr2²		9

   
   

   ∴

   =

   4

   πr1³

   V1

   3

   =

   r1

   ³

   =

   2

   ³

   ×

   8

   or 8 : 27

   V2

   4

   πr2³

   r2

   3

   27

   3

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397. A sphere and a hemisphere have the same volume. The ratio of their radii is
     

1. 1. 1 : 2
      

   
   
   

   2. 1 : 8
      

   
   
   

   3. 1 : √2
      

   
   
   

   4. 1 : ³√2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the radius of sphere be r₁ units and that of hemisphere be r₂ units,
   then,

   	4	πr1³ =	2	πr2³
   	3		3

   
   

   ⇒			r1		³	=	1
   			r2				2

   
   

   =	r1	=	1	or 1 : ³√2
   	r2		³√2

   Correct Option: D

   Let the radius of sphere be r₁ units and that of hemisphere be r₂ units,
   then,

   	4	πr1³ =	2	πr2³
   	3		3

   
   

   ⇒			r1		³	=	1
   			r2				2

   
   

   =	r1	=	1	or 1 : ³√2
   	r2		³√2

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398. A solid sphere of 6 cm diameter is melted and recast into 8 solid spheres of equal volume. The radius (in cm) of each small sphere is
     

1. 1. 1.5
      

   
   
   

   2. 3
      

   
   
   

   3. 2
      

   
   
   

   4. 2.5

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of original sphere =	4	πr³=	4	π × 3 × 3 × 3 = 36π cu.cm.
   	3		3

   
   

   ∴ 8 ×	4	πr1³ = 36π
   	3

   
   

   ⇒ r1³ =	36 × 3	=	27
   	8 × 4		8

   
   

   ⇒r1 = ³√	27	=	3
   	8		2

   
   = 1.5 cm

   Correct Option: A

   Volume of original sphere =	4	πr³=	4	π × 3 × 3 × 3 = 36π cu.cm.
   	3		3

   
   

   ∴ 8 ×	4	πr1³ = 36π
   	3

   
   

   ⇒ r1³ =	36 × 3	=	27
   	8 × 4		8

   
   

   ⇒r1 = ³√	27	=	3
   	8		2

   
   = 1.5 cm

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399. The radii of the base of a cylinder and a cone are in the ratio √3 : √2 and their heights are in the ratio √2 : √3 . Their volume are in the ratio of
     

1. 1. √3 : √2
      

   
   
   

   2. 3√3 : √2
      

   
   
   

   3. √3 : 2√2
      

   
   
   

   4. √2 : √6

   
   
   

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1. View Hint View Answer Discuss in Forum

   	Volume of cylinder
   	Volume of cone

   
   

   =	πr1²h1		= 3.		r1		²		h1
   	1	πr2²h2			r2				h2
   	3

   
   

   = 3 ×		√3		²	×	√2
   		√2				√3

   
   

   = 3 ×	√3	= 3√3 : √2
   	√2

   Correct Option: B

   	Volume of cylinder
   	Volume of cone

   
   

   =	πr1²h1		= 3.		r1		²		h1
   	1	πr2²h2			r2				h2
   	3

   
   

   = 3 ×		√3		²	×	√2
   		√2				√3

   
   

   = 3 ×	√3	= 3√3 : √2
   	√2

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400. Area of the base of a pyramid is 57 sq.cm. and height is 10 cm, then its volume (in cm³), is
     

1. 1. 570
      

   
   
   

   2. 390
      

   
   
   

   3. 190
      

   
   
   

   4. 590

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of the pyramid =	1	× height × area of the base
   	3

   
   

   =	1	× 10 × 57 = 190 cu.cm.
   	3

   Correct Option: C

   Volume of the pyramid =	1	× height × area of the base
   	3

   
   

   =	1	× 10 × 57 = 190 cu.cm.
   	3

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