541. A solid hemisphere is of radius 11 cm. The curved surface area in sq. cm is
     

1. 1. 1140.85
      

   
   
   

   2. 1386.00
      

   
   
   

   3. 760.57
      

   
   
   

   4. 860.57

   
   
   

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1. View Hint View Answer Discuss in Forum

   Curved surface area of hemisphere = 2πr²
   

   = 2 ×	22	× 11 × 11
   	7

   
   = 760.57 sq.cm.

   Correct Option: C

   Curved surface area of hemisphere = 2πr²
   

   = 2 ×	22	× 11 × 11
   	7

   
   = 760.57 sq.cm.

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542. If the radius of a sphere be doubled, the area of its surface will become
     

1. 1. Double
      

   
   
   

   2. Three times
      

   
   
   

   3. Four times
      

   
   
   

   4. None of the mentioned

   
   
   

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1. View Hint View Answer Discuss in Forum

   Original surface area of sphere = πr²
   ⇒ Surface area of sphere = 4π(2r)²
   = 16πr² = 4 × 4πr² = 4 (original surface area)

   Correct Option: C

   Original surface area of sphere = πr²
   ⇒ Surface area of sphere = 4π(2r)²
   = 16πr² = 4 × 4πr² = 4 (original surface area)

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543. A sphere and a hemisphere have the same volume. The ratio of their curved surface area is :
     

1. 1. 2³/₂ : 1
      

   
   
   

   2. 2²/₃ : 1
      

   
   
   

   3. 4³/₂ : 1
      

   
   
   

   4. 2¹/₃ : 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   	4	πr³ =	2	πr1³
   	3		3

   
   [r₁ being the radius of hemisphere]
   

   ⇒ 2r³ = r1³ ⇒	r	=	1
   	r1		2¹/3

   
   

   Required ratio =	4πr²	= 2		r		²	= 2		1		²
   	2πr1²			r1					2¹/3

   
   = 2 × 2²/₃ : 1 = 2¹/₃ : 1

   Correct Option: D

   	4	πr³ =	2	πr1³
   	3		3

   
   [r₁ being the radius of hemisphere]
   

   ⇒ 2r³ = r1³ ⇒	r	=	1
   	r1		2¹/3

   
   

   Required ratio =	4πr²	= 2		r		²	= 2		1		²
   	2πr1²			r1					2¹/3

   
   = 2 × 2²/₃ : 1 = 2¹/₃ : 1

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544. The volume of a solid hemisphere is 19404 cm³. Its total surface area is
     

1. 1. 4158 cm²
      

   
   
   

   2. 2858 cm²
      

   
   
   

   3. 1738 cm²

   
   
   

   4. 2038 cm²

   
   
   

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1. View Hint View Answer Discuss in Forum

   	2	πr³ = 19404
   	3

   
   

   ⇒	2	×	22	× r³ = 19404
   	3		7

   
   

   ⇒ r³ =	19404 × 3 × 7	= 9261
   	2 × 22

   
   ⇒ r = ³√21 × 2 × 21 = 21 cm.
   ∴ Total surface area = 3πr²
   

   = 3 ×	22	× 21 × 21 = 4150 sq.cm.
   	7

   Correct Option: A

   	2	πr³ = 19404
   	3

   
   

   ⇒	2	×	22	× r³ = 19404
   	3		7

   
   

   ⇒ r³ =	19404 × 3 × 7	= 9261
   	2 × 22

   
   ⇒ r = ³√21 × 2 × 21 = 21 cm.
   ∴ Total surface area = 3πr²
   

   = 3 ×	22	× 21 × 21 = 4150 sq.cm.
   	7

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545. The volume of two spheres are in the ratio 8 : 27. The ratio of their surface area is :
     

1. 1. 4 : 9
      

   
   
   

   2. 2 : 3
      

   
   
   

   3. 4 : 5
      

   
   
   

   4. 5 : 6

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the volume be 8x³ and 27x³
   ⇒ Their radius are 2x and 3x
   ∴ The ratio of their surface area = 4x² : 9x² = 4 : 9

   Correct Option: A

   Let the volume be 8x³ and 27x³
   ⇒ Their radius are 2x and 3x
   ∴ The ratio of their surface area = 4x² : 9x² = 4 : 9

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