Question

27 small cubic blocks of side 1 m are joined to form a bigger cube. Now, if one block is removed from each corner of the bigger cube, what will be the surface area (in m${}^2$) of the resultant object?

• A. 54
• B. 46
• C. 30
• D. 27

Answer 1

The correct option is A 54

Volume of one small cube = $sid{e}^3$ = $1^3$ = $1m^3$
Volume of the large cube = $27\times$ volume of small cube = $27\times 1$ = $27m^3$
Side of the large cube = $\sqrt[3]{3volume}$ = $\sqrt[3]{327}$ = 3 m

When a corner cube is removed, the surface area gets rerduced by area of 3 square faces. But, the surface area gets increased by the area of the 3 new square faces formed in the gap created by removal of the cube.
$\therefore$ Change in surface area = Increase by area of 3 square faces + Decrease by area of 3 square faces
= No change

$\therefore$ New surface area = Initial surface area
= $6sid{e}^2$
= $6\times 3^2$
= $54m^2$