Question

64 smaller but identical cubes have been put together to form a larger cube. This larger cube is now painted on all 6 faces. How many of the smaller cubes have exactly two faces painted?

Answer 1

Given : 64 smaller but identical cubes have been put together to form a larger cube

This larger cube is now painted on all 6 faces

To Find : How many of the smaller cubes have exactly two faces painted

Solution:

64 smaller but identical cubes have been put together to form a larger cube.

New cube Size  = 4 x 4 x  4

Cubes at Edges  will have 2 or more Face painted

Cubes at corners will have 3 face painted

Hence at each edge  4 - 2 = 2 cubes will have 2 face painted

there are 12 Edges in Cube

Hence 12 x 2  = 24  cubes

24 smaller cubes have exactly two faces painted

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