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6.
A rectangular tank is 30 m long 20 m broad. Water is being flown into it through a square pipe of side 5 cm. What is the speed of water if the level of water in the tank rises by 1 m in 8 hours?
  • A.
    30 km/hr
  • C.
    40 km/hr
  • B.
    36 km/hr
  • D.
    None of these
  • Answer & Explanation
  • Report
Answer : [A]
Explanation :
Volume of water collected in the tank in 8 hours = 30m x 20m x 1m
  = 600 cu m.  
 
 
  Volume of water collected in the tank in 1 hour =
600
8
 = 75 cu m.  
Water comes through a pipe of cross-section = 5cm x 5cm =
25
10000
 sq m.      
The speed of water = Distance traveled by the water in the pipe in one hour    
  =
75 x 10000
25
 m = 30 km/hr.    
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7.
A rectangular tank is 30 m long 20 m broad. Water is being flown into it through a square pipe of side 5 cm. What is the speed of water if the level of water in the tank rises by 1 m in 8 hours?
  • A.
    30 km/hr
  • C.
    40 km/hr
  • B.
    36 km/hr
  • D.
    None of these
  • Answer & Explanation
  • Report
Answer : [A]
Explanation :
Volume of water collected in the tank in 8 hours = 30m x 20m x 1m
  = 600 cu m.  
 
 
  Volume of water collected in the tank in 1 hour =
600
8
 = 75 cu m.  
Water comes through a pipe of cross-section = 5cm x 5cm =
25
10000
 sq m.      
The speed of water = Distance traveled by the water in the pipe in one hour    
  =
75 x 10000
25
 m = 30 km/hr.    
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8.
How many small cubes, each of 96 sq cms surface area, can be formed from the material obtained by melting a larger cube of 384 cm2 surface area?
  • A.
    8
  • C.
    800
  • B.
    5
  • D.
    8000
  • Answer & Explanation
  • Report
Answer : [D]
Explanation :
Edge of the small cube =
96
6
 = 4m    
Edge of the large cube =
384
6
 = 8 cm    
No. of small cubes =
8 x 8 x 8
4
10
x
4
10
x
4
10
 = 8000.
     
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9.
A cube of lead with edges measuring 6 cm each is melted and recasted into 27 equal cubes. The length of the edge of the new cube is
  • A.
    3 cm
  • C.
    2 cm
  • B.
    4 cm
  • D.
    1.5 cm
  • Answer & Explanation
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Answer : [C]
Explanation :
  Edge of the cube = 6 cm  
 
 
  Volume of lead = 63 cm3 = 216 cm3  
  Let the edge of the new cube be x cm  
  Then 27x3 = 216  
   
 
 
  x3 = 8 or x = 2 cm.  
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10.
Find the weight of a hollow cylindrical lead pipe 28 cm long and
1
2
 cm think. Its internal
diameter is 8 cm.   Weight of 1 cm3 of lead is 11.4 g, Π =
22
7
   
  • A.
    3.762 kg
  • C.
    7.462 kg
  • B.
    4.562 kg
  • D.
    6.762 kg
  • Answer & Explanation
  • Report
Answer : [A]
Explanation :
External radius of the pipe =
8
4
 = 4 cm    
  External volume = r2h
  =  
22
7
 x 4 x 4 x 28        
  = 1408 cu cm  
  Internal diameter = 8 – 1 = 7 cm  
  Internal radius =
7
2
 = 3.5 cm      
  Internal volume = r2h
  =  
22
7
 x 3.5 x 3.5 x 28        
  = 1078 cu cm.  
  Weight of lead = 330 x 11.4 = 3762 g  
  = 3.762 kg.  
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