A hollow cube of size 5cm is taken, with the thickness of 1cm. It is made of smaller cubes of size 1cm .If the outer surface of the cube is painted how many faces of the smaller cubes remain unpainted? Select
A) 438
B) 550
C) 500
D) 450
E) 498
Volume of Big Cube considering it is not hollow = L3 = 5*5*5= 
<gadget id="calculator">5*5*5</gadget>
<output>125</output>
125 cm3   Size of hollow cube (considering 1 cm thickness on two faces of large cube= 5 - 2= 
<gadget id="calculator">5 - 2</gadget>
<output>3</output>
3cm   Volume of hollow cube= 3*3*3= 
<gadget id="calculator">3*3*3</gadget>
<output>27</output>
27 cm3   So Total Volume filled up by smaller cubes= Volume of Larger Cube - Volume of hollow cube   = 125 - 27= 
<gadget id="calculator">125 - 27</gadget>
<output>98</output>
98 cm3   Volume of 1 small cube= 1*1*1= 
<gadget id="calculator">1*1*1</gadget>
<output>1</output>
1 cm3   Total number of small cubes in the larger cube= 98 / 1= 
<gadget id="calculator">98 / 1</gadget>
<output>98</output>
98   and Number of faces of 98 small cubes (6 faces each cube has)= 98*6= 
<gadget id="calculator">98*6</gadget>
<output>588</output>
588 faces   Total Surface area of 6 faces of larger cube painted= 6*L2 = 6*5*5= 
<gadget id="calculator">6*5*5</gadget>
<output>150</output>
150cm2   Surface area of one face of small cube= 1*1= 
<gadget id="calculator">1*1</gadget>
<output>1</output>
1cm2   Number of faces of small cube painted= 150/1= 
<gadget id="calculator">150/1</gadget>
<output>150</output>
150 faces   Hence number of faces of the smaller cubes remain unpainted= 588-150= 
<gadget id="calculator">588-150</gadget>
<output>438</output>
438   answer.438
<result>A</result>
A hollow cube of size 5cm is taken, with the thickness of 1cm. It is made of smaller cubes of size 1cm .If the outer surface of the cube is painted how many faces of the smaller cubes remain unpainted?