Latest TCS Aptitude Question SOLUTION: Anita make cube with dimension 5*5*5 using 1*1*1 cubes.find no. Of cubes to make it hollow of same shape.

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Anita make cube with dimension 5*5*5 using 1*1*1 cubes.find no. Of cubes to make it hollow of same shape.

Asked In TCS manu (11 years ago)

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Harry Ramsub  (11 years ago)

To make the 5*5*5 hollow, the inner cubic part must be removed. This would constitute one cube each from front,back,top,bottom,left and right ! Since the 5*5*5 is made up of 1*1*1 cubes, 3*3*3 cubes (i.e. 5-2*5-2*5-2) would have to be removed to make it hollow with the shape retained. 27 cubes would be removed, remaining 125-27=98.

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dia  (11 years ago)

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 4 faces of the outer surface of the cube are painted, totally how many faces of the smaller cubes remain unpainted?

Side of cube = 5 cm and its thickness = 1 cm
so volume of outer cube = 5*5*5 volume of inner cube = 3*3*3 (as 1cm is taken off at both ends)
volume of the hollow cube = 5*5*5 - 3*3*3 = 125-27 = 98
So total no of small cubes of the size 1 cm = 98/1*1*1 = 98

we know a cube has 6 faces so total no of face = 98*6 = 588
One surface of outer cube contains a total of 25 surface of smaller cube , so when 4 surfaces of outer cube is painted total no of surface of small cubes i.e supposed to be painted is 4*25 = 100

So the total no of surfaces of small cube that will be remained unpainted is 588-100 = 488

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