781. If radius of a circle is increased by 5%, then the increase in its area is
     

1. 1. 10.25 %
      

   
   
   

   2. 10 %
      

   
   
   

   3. 5.75 %
      

   
   
   

   4. 5 %

   
   
   

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1. View Hint View Answer Discuss in Forum

   Using Rule 12,
   

   Required per cent increase =		2x +	x²		%
   			100

   
   

   =		2 × 5 +	5 × 5		%
   			100

   
   = 10.25 %

   Correct Option: A

   Using Rule 12,
   

   Required per cent increase =		2x +	x²		%
   			100

   
   

   =		2 × 5 +	5 × 5		%
   			100

   
   = 10.25 %

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782. The ratio of radii of two cone is 3 : 4 and the ratio of their height is 4 : 3. Then the ratio of their volume will be
     

1. 1. 3 : 4
      

   
   
   

   2. 4 : 3
      

   
   
   

   3. 9 : 16
      

   
   
   

   4. 16 : 9

   
   
   

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1. View Hint View Answer Discuss in Forum

   ∴

   =

   1

   πr1²h1

   V1

   3

   =

   r1

   ²

   ×

   h1

   =

   3

   ²

   ×

   4

   V2

   1

   πr²h2

   r2

   h2

   4

   3

   3

   
   

   =	3	×	3	×	3	=	3	⇒ 3 : 4
   	4		4		4		4

   Correct Option: A

   ∴

   =

   1

   πr1²h1

   V1

   3

   =

   r1

   ²

   ×

   h1

   =

   3

   ²

   ×

   4

   V2

   1

   πr²h2

   r2

   h2

   4

   3

   3

   
   

   =	3	×	3	×	3	=	3	⇒ 3 : 4
   	4		4		4		4

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783. If the height of a given cone be doubled and radius of the base remains the same, the ratio of the volume of the given cone to that of the second cone will be
     

1. 1. 2 : 1
      

   
   
   

   2. 1 : 8
      

   
   
   

   3. 1 : 2
      

   
   
   

   4. 8 : 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   Case I : When height = h₁, radius = r₁,
   

   Volume of the cone V1 =	1	πr1²h1
   	3

   
   Case II,
   When height h₂ = 2h₁,
   radius r² = r₁ [radius is same] Volume of the cone
   

   V2 =	1	πr2²h2
   	3

   
   ∴ The required ratio = 1 : 2

   Correct Option: C

   Case I : When height = h₁, radius = r₁,
   

   Volume of the cone V1 =	1	πr1²h1
   	3

   
   Case II,
   When height h₂ = 2h₁,
   radius r² = r₁ [radius is same] Volume of the cone
   

   V2 =	1	πr2²h2
   	3

   
   ∴ The required ratio = 1 : 2

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784. If the radius of the base of a cone be doubled and height is left unchanged, then ratio of the volume of new cone to that of the original cone will be :
     

1. 1. 1 : 4
      

   
   
   

   2. 2 : 1
      

   
   
   

   3. 1 : 2
      

   
   
   

   4. 4 : 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of original cone, Vl =	1	πr²h
   	3

   
   Now, radius of new cone, r₁= 2r
   height, h₁ = h
   

   ∴ Volume V2 =	1	πr1²h1
   	3

   
   

   =	1	π(2r)² × h =	4	πr²h
   	3		3

   
   

   ∴		=	4	πr²h
   	V2		3
   	V1		1	πr²h
   			3

   
   = 4 : 1

   Correct Option: D

   Volume of original cone, Vl =	1	πr²h
   	3

   
   Now, radius of new cone, r₁= 2r
   height, h₁ = h
   

   ∴ Volume V2 =	1	πr1²h1
   	3

   
   

   =	1	π(2r)² × h =	4	πr²h
   	3		3

   
   

   ∴		=	4	πr²h
   	V2		3
   	V1		1	πr²h
   			3

   
   = 4 : 1

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785. Each of the measure of the radius of base of a cone and that of a sphere is 8 cm. Also, the volume of these two solids are equal. The slant height of the cone is
     

1. 1. 8√17 cm
      

   
   
   

   2. 4√17 cm
      

   
   
   

   3. 34√2 cm
      

   
   
   

   4. 34 cm.

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of sphere =	4	π × 8³ = Volume of cone
   	3

   
   

   Volume of cone =	4	π r²h
   	3

   
   

   ∴	1	× π × 8 × 8 × h
   	3

   
   

   =	4	× π × 8³
   	3

   
   ⇒ h= 32 cm.
   ∴ Slant height = √h² + r² = √32² + 8² = √1024 + 64
   = √64(16 + 1) = 8√17 cm.

   Correct Option: A

   Volume of sphere =	4	π × 8³ = Volume of cone
   	3

   
   

   Volume of cone =	4	π r²h
   	3

   
   

   ∴	1	× π × 8 × 8 × h
   	3

   
   

   =	4	× π × 8³
   	3

   
   ⇒ h= 32 cm.
   ∴ Slant height = √h² + r² = √32² + 8² = √1024 + 64
   = √64(16 + 1) = 8√17 cm.

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