Question

Consider a big cube formed of 64 smaller cubes of which 40 are coloured. The smaller cubes are arranged such that the exposure of the coloured cubes to the outside is minimised
What is the percentage of the exposed area that is coloured?

62.5%
50%
41.6%
None of these
​

Answer 1

Given :   a big cube formed of 64 smaller cubes of which 40 are coloured.

The smaller cubes are arranged such that the exposure of the coloured cubes to the outside is minimised

To Find : What is the percentage of the exposed area that is coloured?

62.5%

50%

41.6%

None of these

Solution:

a big cube formed of 64 smaller cubes

Then big cube = 4 * 4  * 4

Cubes no face expose  = (4 - 2)(4 - 2)(4 - 2) = 8

Cubes 1 face expose  = 6(4 - 2)(4 - 2) =24

Cubes 2 face expose = 12 * (4 -2 )  = 24

Cubes 3 face expose  =  8  

out of 40 colored cubes   8 with  no face expose , 24 with 1 face expose

and 2 face expose = 40 - (8 + 24)  = 8

Total Face exposed

8 * 0  + 24 * 1  + 8 * 2 = 40  

Total faces of cube = 6 * 4²  = 96   sq units

Exposed area  = 100 * 40 /96

= 41.67 %

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