Hi
rishabhjain13I am not considering exposed sides as per the diagram.
even the bottom ones are considered.
lets calculate colored (exposed) area again,
Now how many cubes do we have?
27
how many are exposed?
26. (all except the one at the center)
for each exposed cube, how many faces are colored?
1 (given that Each of 27 white cubes will have exactly one face painted red)
since we are calculating greatest possible surface area that could be red,
Maximum red faces can be 27 * 1 = 27 but one red face for the cube at the center can never be exposed.
so maximum red surface exposed will be 26.
(imagine arrangement where in colored side of each cube is exposed/facing outward).
To calculate fraction, we need to divide this with total surface exposed in a cube (painted or not painted)
total surface area exposed in a cube = number of faces in big cube * no of faces of 1-centimeter cubes in each face of big cube
= 6 * 9 ( you can understand this from the diagram)
= 54
ans = 26/54
=13/27
I hope its clear. Maybe experts can explain it in a better manner.
Regards,