by Anil Babbur - Wednesday, 5 January 2011, 10:09 PM

A hollow cube of size 5 cm is taken, with a thickness of 1 cm. It is made of smaller cubes of size 1 cm. If one face of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?
a) 900 b) 488 c) 563 d) 800

There are 5^{3} - 3^{3} = 98 smaller cubes being used with a total of 6*98 = 588 faces and out of which 5^{2} = 25 faces are painted which leaves 588 - 25 = 563 unpainted faces of the smaller cubes.