466. How many cubes, each of edge 3 cm, can be cut from a cube of edge 15 cm?
     

1. 1. 25
      

   
   
   

   2. 27
      

   
   
   

   3. 125
      

   
   
   

   4. 144

   
   
   

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1. View Hint View Answer Discuss in Forum

   No. of Cubes =	Volume of larger cube
   	Volume of smaller cube

   
   

   =	(15)³	=	15 × 15 × 15	= 5 × 5 × 5 = 125
   	(3)³		3 × 3 × 3

   Correct Option: C

   No. of Cubes =	Volume of larger cube
   	Volume of smaller cube

   
   

   =	(15)³	=	15 × 15 × 15	= 5 × 5 × 5 = 125
   	(3)³		3 × 3 × 3

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467. A right cylindrical vessel is full with water. How many right cones having the same diameter and height as that of the right cylinder will be needed to store that water ? (Take π = 22/7)
     

1. 1. 4
      

   
   
   

   2. 2
      

   
   
   

   3. 3
      

   
   
   

   4. 5

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of cylindrical vessel = πr²h
   

   Volume of cone =	1	πr²h
   	3

   
   

   ∴ Number of cones =	πr²h		= 3
   	1	πr²h
   	3

   Correct Option: C

   Volume of cylindrical vessel = πr²h
   

   Volume of cone =	1	πr²h
   	3

   
   

   ∴ Number of cones =	πr²h		= 3
   	1	πr²h
   	3

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468. Marbles of diameter 1.4 cm are dropped into a cylindrical beaker containing some water and are fully submerged. The dia meter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm ?
     

1. 1. 50
      

   
   
   

   2. 150
      

   
   
   

   3. 250
      

   
   
   

   4. 350

   
   
   

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1. View Hint View Answer Discuss in Forum

   Volume of raised water in cylindrical beaker
   

   = πr²h =	22	×	7	×	7	× 5.6
   	7		2		2

   
   = 215.6 cu.cm.
   

   Volume of a marble =	4	πr³
   	3

   
   

   =	4	×	22	× (0.7)³ =	4.312	cu.cm.
   	3		7		3

   
   

   ∴ Number of marbles =	215.6		=	215.6 × 3	= 150
   	4.312			4.312
   	3

   Correct Option: B

   Volume of raised water in cylindrical beaker
   

   = πr²h =	22	×	7	×	7	× 5.6
   	7		2		2

   
   = 215.6 cu.cm.
   

   Volume of a marble =	4	πr³
   	3

   
   

   =	4	×	22	× (0.7)³ =	4.312	cu.cm.
   	3		7		3

   
   

   ∴ Number of marbles =	215.6		=	215.6 × 3	= 150
   	4.312			4.312
   	3

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469. The diameter of the base of a cylindrical drum is 35 dm. and the height is 24 dm. It is full of kerosene. How many tins each of size 25 cm × 22 cm × 35 cm can be filled with kerosene from the drum? (Use π = 22/7)
     

1. 1. 1200
      

   
   
   

   2. 1020
      

   
   
   

   3. 600
      

   
   
   

   4. 120

   
   
   

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1. View Hint View Answer Discuss in Forum

   Required number of tins =	Volume of cylindricaldrum
   	volume of a tin

   
   

   =	22 × 350 × 350 × 240	= 1200
   	7 × 2 × 2 × 25 × 22 × 35

   Correct Option: A

   Required number of tins =	Volume of cylindricaldrum
   	volume of a tin

   
   

   =	22 × 350 × 350 × 240	= 1200
   	7 × 2 × 2 × 25 × 22 × 35

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470. The circumference of the base of a circular cylinder is 6π cm. The height of the cylinder is equal to the diameter of the base. How many litres of water can it hold?
     

1. 1. 54π cc
      

   
   
   

   2. 36π cc
      

   
   
   

   3. 0.054π cc
      

   
   
   

   4. 0.54π cc

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let Circumference of base = πd
   ⇒ πd = 6π ⇒ d = 6 cm
   ∴ Height, h = 6 cm
   Volume of the cylinder,
   

   V =	πr²h	=	πd³	=	π(6)³	cc = 54π cc
   	4		4		4

   Correct Option: A

   Let Circumference of base = πd
   ⇒ πd = 6π ⇒ d = 6 cm
   ∴ Height, h = 6 cm
   Volume of the cylinder,
   

   V =	πr²h	=	πd³	=	π(6)³	cc = 54π cc
   	4		4		4

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