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Q.

The internal dimensions of the box are 1.2 m, 80 cm and 50 cm. How many cubes each of edge 7 cm can be packed in the box with faces parallel to the sides of the box .Also find the empty space left in the box.


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a

1758,143 cm 3  

b

1399,143 cm 3  

c

1638,143 cm 3  

d

1589,143 cm 3   

answer is B.

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Detailed Solution

Given information
IMG_256
The dimensions of the cuboidal box are as follows,
Length of the box ,
l=1.2 m l=1.2×100 cm l = 120 cm  
Breadth of the box,
b=80cm  
Height of the box,
h=50cm  
Volume of the bigger cuboidal box is given by,
⇒ V 1 =l×b×h⋯(1)  
⇒ V 1 =120×80×50 ⇒ V 1 =480000 c m 3  
The edge of the cubical box is,
⇒a=7 cm  
The volume of the cube is given by,
⇒ V 2 = a 3 ⋯ 2  
Substitute the value of in equation (2), we get
⇒ V 2 = (7) 3 ⇒ V 2 =343 c m 3  
The number of smaller cubical boxes that can be accommodated in the bigger cuboidal box is given by,
⇒n= V 1 V 2 ⋯(3)  
⇒n= 480000 343 ⇒n=1399.417  
Complete boxes that fit in the box are, Question Image.
It is quite evident that the cube box does not fully occupy the cube box. This is because the value is rounded to the largest integer. The 0.417 part corresponds to the empty space in the cuboid box.
The empty space is given by
⇒E= V 1 −n V 2 ⋯(4)  
Substitute the obtained values in equation (4), we get
⇒E=480000−1399×343 ⇒E=143 c m 3  
Thus, the number of boxes are  n=1399   and the empty space is, E=143c m 3  .
So, option 2 is correct.
 
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