436. If the height and the radius of the base of a cone are each increased by 100%, then the volume of the cone becomes
     

1. 1. double that of the original
      

   
   
   

   2. three times that of the original
      

   
   
   

   3. six times that of the original
      

   
   
   

   4. eight times that of the original

   
   
   

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1. View Hint View Answer Discuss in Forum

   For original cone,
   

   V =	1	πr²h
   	3

   
   For the second cone,
   r₁ = 2r
   h₁ = 2h
   

   ∴ V1 =	1	πr1²h1
   	3

   
   

   =	1	π(2r)² × 2h
   	3

   
   

   = 8 ×	1	πr²h = 8 V
   	3

   Correct Option: D

   For original cone,
   

   V =	1	πr²h
   	3

   
   For the second cone,
   r₁ = 2r
   h₁ = 2h
   

   ∴ V1 =	1	πr1²h1
   	3

   
   

   =	1	π(2r)² × 2h
   	3

   
   

   = 8 ×	1	πr²h = 8 V
   	3

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437. If the radius of a right circular cylinder is decreased by 50% and its height is increased by 60%, its volume will be decreased by
     

1. 1. 10%
      

   
   
   

   2. 60%
      

   
   
   

   3. 40%
      

   
   
   

   4. 20%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the radius of a right circular cylinder is changed by x% and height is changed y%, then Volume change by
   

   		2x + y +	x² + 2xy	+	x²y		%
   			100		100²

   
   

   ∴ Effective change =		- 2 × 50 + 60 +	2500 - 6000	+	150000		%
   			100		10000

   
   = (–100 + 60 – 35 + 15)
   = (75 – 135) = – 60%
   Negative sign shows decrease.

   Correct Option: B

   Let the radius of a right circular cylinder is changed by x% and height is changed y%, then Volume change by
   

   		2x + y +	x² + 2xy	+	x²y		%
   			100		100²

   
   

   ∴ Effective change =		- 2 × 50 + 60 +	2500 - 6000	+	150000		%
   			100		10000

   
   = (–100 + 60 – 35 + 15)
   = (75 – 135) = – 60%
   Negative sign shows decrease.

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438. A copper sphere of diameter 18 cm is drawn into a wire of diameter 4 mm. The length of the wire, in metre, is :
     

1. 1. 2.43
      

   
   
   

   2. 243
      

   
   
   

   3. 2430
      

   
   
   

   4. 24.3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of sphere =	4	πr³
   	3

   
   

   =	4	π × 9 × 9 × 9
   	3

   
   = 972π cubic.cm.
   If the length of wire be h cm., then
   π × (0.2)² × h = 972π
   

   ⇒ h =	972	= 24300 cm.
   	0.2 × 0.2

   
   or 243 metres

   Correct Option: B

   Volume of sphere =	4	πr³
   	3

   
   

   =	4	π × 9 × 9 × 9
   	3

   
   = 972π cubic.cm.
   If the length of wire be h cm., then
   π × (0.2)² × h = 972π
   

   ⇒ h =	972	= 24300 cm.
   	0.2 × 0.2

   
   or 243 metres

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439. Each of the radius of the base and the height of a right circular cylinder is increased by 10%. The volume of the cylinder is increased by
     

1. 1. 3.31%
      

   
   
   

   2. 14.5%
      

   
   
   

   3. 33.1%
      

   
   
   

   4. 19.5%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Intial area of the cylinder = πr²h
   Voiume of the new cylinder = p (1.1r)² × 1.1h
   = 1.331 πr²h
   ∴ Increase in area = (1.331 – 1) πr²h
   = 0.331 πr²h
   

   ∴ Percentage increase =	0.331πr²h	× 100 = 33.1 %
   	πr²h

   Correct Option: C

   Intial area of the cylinder = πr²h
   Voiume of the new cylinder = p (1.1r)² × 1.1h
   = 1.331 πr²h
   ∴ Increase in area = (1.331 – 1) πr²h
   = 0.331 πr²h
   

   ∴ Percentage increase =	0.331πr²h	× 100 = 33.1 %
   	πr²h

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440. If the height of a cone is increased by 100% then its volume is increased by :
     

1. 1. 100%
      

   
   
   

   2. 200%
      

   
   
   

   3. 300%
      

   
   
   

   4. 400%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of the cone =	1	πr²h, new height = 100%h
   	3

   
   ∴ Percentage increase in volume = 100%

   Correct Option: A

   Volume of the cone =	1	πr²h, new height = 100%h
   	3

   
   ∴ Percentage increase in volume = 100%

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