A big cube is formed by rearranging the 160 coloured and 56

prab.sahi01 wrote:A big cube is formed by rearranging the 160 coloured and 56 non-coloured similar cubes in such a way that the exposure of the coloured cubes to the outside is minimum. The percentage of exposed area to the coloured is :

A. 25.9%
B. 44.44%
C. 35%
D. 61%
E. None of these

Can someone help me with this ??

Minimising the surface area of coloured cubes means maximising the surface area of uncoloured cubes in the big cube.
Since all cubes are similar, total cubes is 160+56=216 and if we take the length of cube as 1 unit,then total surface area will be 6x (length)xlength=216 units

Now in any big cube, maximum surface area exposed will be at 8 corners where 3 surfaces of small cubes will be exposed and then 2 surfaces of all small cubes along all the edges of the big cube will be exposed thereafter. this gives total surface area as

8 corners of big cube x 3 unit area (surfaces) of small cube at each corner + 2 unit area (surfaces) of small cube x 4 such small cubes at each edge of big cube
= 8 X 3 + 2 x 4 x 12 (total edges of a cube is 12)
=120 (max surface area of uncoloured cubes)

So total surface area of coloured cubes will be 216-120= 96
and hence the percentage will be 96/216= 44.44%