431. A cone of height 7 cm and base radius 1 cm is carved from a cuboidal block of wood 10 cm × 5cm × 2 cm. [Assuming π = 22/7] The percentage wood wasted in the process is :
     

1. 1. 92	2	%
      	3

      
      

   
   
   

   2. 46	1	%
      	3

   
   
   

   3. 53	2	%
      	3

   
   
   

   4. 7	1	%
      	3

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of cone =	1	πr²h =	1	×	22	× 1 × 7 =	22	cu.cm.
   	3		3		7		3

   
   Volume of cubical block = 10 × 5 × 2 cm³. = 100 cm³.
   

   Wastage of wood =		100 -	22		cm³ =	300 - 22	=	278	cm³
   			3			3		3

   
   ´

   ∴ % Wastage =	278	× 100
   	3
   	100

   
   

   =	278	= 92	2	%
   	3		3

   Correct Option: A

   Volume of cone =	1	πr²h =	1	×	22	× 1 × 7 =	22	cu.cm.
   	3		3		7		3

   
   Volume of cubical block = 10 × 5 × 2 cm³. = 100 cm³.
   

   Wastage of wood =		100 -	22		cm³ =	300 - 22	=	278	cm³
   			3			3		3

   
   ´

   ∴ % Wastage =	278	× 100
   	3
   	100

   
   

   =	278	= 92	2	%
   	3		3

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432. If the radius of a cylinder is decreased by 50% and the height is increased by 50% to form a new cylinder, the volume will be decreased by
     

1. 1. 0%
      

   
   
   

   2. 25%
      

   
   
   

   3. 62.5%
      

   
   
   

   4. 75%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Required percentage decrease = 100 -	50 × 50 × 150	= 100 - 37.5 = 62.5 %
   	100 × 100

   Correct Option: C

   Required percentage decrease = 100 -	50 × 50 × 150	= 100 - 37.5 = 62.5 %
   	100 × 100

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433. Each of the height and base-radius of a cone is increased by 100%. The percentage increase in the volume of the cone is
     

1. 1. 700%
      

   
   
   

   2. 400%
      

   
   
   

   3. 300%
      

   
   
   

   4. 100%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Required per cent
   

   ∴	200 × 200 × 200	- 100 = 800 - 100 = 700 %
   	100 × 100

   Correct Option: A

   Required per cent
   

   ∴	200 × 200 × 200	- 100 = 800 - 100 = 700 %
   	100 × 100

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434. If both the radius and height of a right circular cone are increased by 20%, its volume will be increased by
     

1. 1. 20%
      

   
   
   

   2. 40%
      

   
   
   

   3. 60%
      

   
   
   

   4. 72.8%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let height and radius both of a cylinder change by x%, then volume changes by
   

   3x +

   3x²

   +

   x³

   % =

   3 × 20 +

   3 × 20 × 20

   +

   20 × 20 × 20

   %

   100

   100²

   100

   10000

   
   = (60 + 12 + 0.8)% = 72.8%

   Correct Option: D

   Let height and radius both of a cylinder change by x%, then volume changes by
   

   3x +

   3x²

   +

   x³

   % =

   3 × 20 +

   3 × 20 × 20

   +

   20 × 20 × 20

   %

   100

   100²

   100

   10000

   
   = (60 + 12 + 0.8)% = 72.8%

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435. If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, the volume of the

1. 1. cone increases by 25%
      

   
   
   

   2. increases by 50%
      

   
   
   

   3. remains unaltered
      

   
   
   

   4. decreases by 25%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of original cone =	1	πr²h
   	3

   
   Now, r₁ = radius of new cone = r/2
   h₁ = height of new cone = 3h
   

   ∴ V1 =	1	πr1²h1 =	1	π	r²	× 3h =	1	πr²h ×	3	=	3	V
   	3		3		4		3		4		4

   
   

   ∴ Decrease % =		V -	3	V		× 100
   			4
   			V

   
   = 25%

   Correct Option: D

   Volume of original cone =	1	πr²h
   	3

   
   Now, r₁ = radius of new cone = r/2
   h₁ = height of new cone = 3h
   

   ∴ V1 =	1	πr1²h1 =	1	π	r²	× 3h =	1	πr²h ×	3	=	3	V
   	3		3		4		3		4		4

   
   

   ∴ Decrease % =		V -	3	V		× 100
   			4
   			V

   
   = 25%

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