Question

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?

• A. $225c{m}^2$
• B. $234c{m}^2$
• C. $270c{m}^2$
• D. $279c{m}^2$

Answer 1

The correct option is B $234c{m}^2$

When one cube is pasted on each of 5 faces of a cube then,
Surface are of each cube pasted $=5x^2$
$=5\times (3{)}^{2}c{m}^2$$=45c{m}^2$
For 5 faces, total area $=5\times 45=225c{m}^2$
But surface area of the bottom face where the cube is not pasted $=x^2=3^2=9c{m}^2$
$\therefore$ Total area $=225c{m}^2+9c{m}^2$
$\therefore$ Total area $=225c{m}^2+9c{m}^2=234c{m}^2$