151. How many hemispherical balls can be made from a cylinder 56 cm high and 12 cm diameter, when every ball being 0.75 cm in radius?
     

1. 1. 1792
      

   
   
   

   2. 3584
      

   
   
   

   3. 4824
      

   
   
   

   4. 7168

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of cylinder = πr²h = (π × 6 × 6 × 56) cu. cm.
   

   Volume of hemi-spherical ball =		2	π × 0.75 × 0.75 × 0.75		cubic unit
   		3

   
   

   ∴ Total number of balls =	π × 3 × 3 × 8
   		2	π × 0.75 × 0.75 × 0.75
   		3

   
   = 7168

   Correct Option: D

   Volume of cylinder = πr²h = (π × 6 × 6 × 56) cu. cm.
   

   Volume of hemi-spherical ball =		2	π × 0.75 × 0.75 × 0.75		cubic unit
   		3

   
   

   ∴ Total number of balls =	π × 3 × 3 × 8
   		2	π × 0.75 × 0.75 × 0.75
   		3

   
   = 7168

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152. The number of coins of radius 0.75 cm and thickness 0.2cm required to be melted to make a right circular cylinder of height 8 cm and base radius 3 cm is :
     

1. 1. 500
      

   
   
   

   2. 600
      

   
   
   

   3. 460
      

   
   
   

   4. 640

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of 1 coin = πr²h
   = (π × 0.75 × 0.75 × 0.2) cu. cm.
   Volume of cylinder = (π × 3 × 3 × 8) cu. cm.
   

   ∴ Number of coins =	π × 3 × 3 × 8
   	π × 0.75 × 0.75 × 0.2

   
   

   =	3 × 3 × 8 × 100 × 100 × 10
   	75 × 75 × 2

   
   = 640

   Correct Option: D

   Volume of 1 coin = πr²h
   = (π × 0.75 × 0.75 × 0.2) cu. cm.
   Volume of cylinder = (π × 3 × 3 × 8) cu. cm.
   

   ∴ Number of coins =	π × 3 × 3 × 8
   	π × 0.75 × 0.75 × 0.2

   
   

   =	3 × 3 × 8 × 100 × 100 × 10
   	75 × 75 × 2

   
   = 640

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153. A sphere of radius 5 cm is melted to form a cone with base of same radius. The height (in cm) of the cone is
     

1. 1. 5
      

   
   
   

   2. 10
      

   
   
   

   3. 20
      

   
   
   

   4. 22

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of sphere =	4	πr³
   	3

   
   

   Volume of cone =	1	πr²h
   	3

   
   According to the question,
   

   	1	πr²h =	4	πr³
   	3		3

   
   ⇒ h = 4r = 4 × 5 = 20 cm.

   Correct Option: C

   Volume of sphere =	4	πr³
   	3

   
   

   Volume of cone =	1	πr²h
   	3

   
   According to the question,
   

   	1	πr²h =	4	πr³
   	3		3

   
   ⇒ h = 4r = 4 × 5 = 20 cm.

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154. The diameters of two cylinders are in the ratio 3:2 and their volumes are equal. The ratio of their heights is
     

1. 1. 2 : 3
      

   
   
   

   2. 3 : 2
      

   
   
   

   3. 9 : 4
      

   
   
   

   4. 4 : 9

   
   
   

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1. View Hint View Answer Discuss in Forum

   	d1	=	r1	=	3	V1 = V2
   	d2		r2		2

   
   ⇒ πr₁²h₁ = πr₂²h₂
   

   ⇒

   h1

   =

   r2

   ²

   =

   2

   ²

   =

   4

   h2

   r1

   3

   9

   
   = 4 : 9

   Correct Option: D

   	d1	=	r1	=	3	V1 = V2
   	d2		r2		2

   
   ⇒ πr₁²h₁ = πr₂²h₂
   

   ⇒

   h1

   =

   r2

   ²

   =

   2

   ²

   =

   4

   h2

   r1

   3

   9

   
   = 4 : 9

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155. A cylindrical container of 32 cm height and 18 cm radius is filled with sand. Now all this sand is used to form a conical heap of sand. If the height of the conical heap is 24 cm, what is the radius of its base ?
     

1. 1. 12 cm
      

   
   
   

   2. 24 cm
      

   
   
   

   3. 36 cm
      

   
   
   

   4. 48 cm

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of sand = Volume of cylindrical vessel = πr²h
   = π × (18)² × 32 cu.cm.
   Volume of conical heap = π × 18 × 18 × 32
   

   ⇒	1	πR²H = × π × 18 × 18 × 32
   	3

   
   

   ⇒	1	× R² × 24 = 18 × 18 × 32
   	3

   
   

   ⇒ R² =	18 × 18 × 32 × 3	= 1296
   	24

   
   ⇒ R = √1296 = 36 cm.

   Correct Option: C

   Volume of sand = Volume of cylindrical vessel = πr²h
   = π × (18)² × 32 cu.cm.
   Volume of conical heap = π × 18 × 18 × 32
   

   ⇒	1	πR²H = × π × 18 × 18 × 32
   	3

   
   

   ⇒	1	× R² × 24 = 18 × 18 × 32
   	3

   
   

   ⇒ R² =	18 × 18 × 32 × 3	= 1296
   	24

   
   ⇒ R = √1296 = 36 cm.

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