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?
Correct answer: A
Explanation
Volume of Big Cube considering it is not hollow = L3 = 5*5*5 = 125 cm3
Size of hollow cube (considering 1 cm thickness on two faces of large cube = 5 - 2 = 3cm
Volume of hollow cube = 3*3*3 = 27 cm3
So Total Volume filled up by smaller cubes = Volume of Larger Cube - Volume of hollow cube
= 125 - 27
= 98 cm3
Volume of 1 small cube = 1*1*1 = 1 cm3
Total number of small cubes in the larger cube = 98 / 1 = 98
and Number of faces of 98 small cubes (6 faces each cube has) = 98*6 = 588 faces
Total Surface area of 6 faces of larger cube painted = 6*L2 = 6*5*5 = 150cm2
Surface area of one face of small cube = 1*1 = 1cm2
Number of faces of small cube painted = 150/1 = 150 faces
Hence number of faces of the smaller cubes remain unpainted= 588-150
= 438
answer.A
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