The greatest possible surface area of the prism is 78 square units, it is obtained by removing center cube on each side of the prism.
Explanation:
The given is,
Prism is made up of 27 identical cubes
Step:1
Ref attachment,
Let, surface area of one of cube = 1 square units
Surface area of given prism,
In the given diagram it have 9 cube sides in each side of prism.
1 surface prism = 9 surface of cube
Surface area of given prism = 6 × Surface of prism
= 6 × 9
= 54 square units
Step:2 Check for alternative's
For removing one cube on the edge of prism,
1 surface of prim = 9 surfaces of cube
Surface area after removing cube on each side,
= 6 × 11 = 66 square units
For removing cube on corner of prism,
1 surface of prim = 9 surfaces of cube
Surface area after removing cube on corner,
= 6 × 9 = 54 square units
For removing center cube on each side,
1 surface of prim = 13 surfaces of cube
Surface area after removing cube on corer on the prism,
= 6 × 13 = 78 square units
Surface area after removing corner cube on prism = 78 square units
Result:
The greatest possible surface area of the prism is 78 square units, it is obtained by removing center cube on each side of the prism.