Except for one face of given cube, identical cubes are glued through their faces to all the other faces of the given cube. If each side of the given cube measures 3 cm, then what is the total surface area of the solid thus formed?
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$225 cm^{2}$
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$234 cm^{2}$
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$270 cm^{2}$
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$279 cm^{2}$
B
Correct answer
Explanation
A cube has 6 faces. If we glue cubes to 5 faces, we lose 5 faces of the original cube and 5 faces of the new cubes. Original surface area = 6 * 3^2 = 54. 5 new cubes added, each adds 5 exposed faces. Total surface = 54 + 5 * (5 * 3^2) - 5 * 3^2 (covered area) = 54 + 225 - 45 = 234.