Question

A cube is painted on all of its surface and then divided into $216$ equal smaller cubes. How many smaller cubes will be with none painted surfaces?

• A. $27$
• B. $36$
• C. $64$
• D. $54$

Answer 1

The correct option is C $64$

V(Big cube) = 216 $\times$ V (small cube)

$A^3=216a^3$

$(\frac{A}{216}{)}^3=a$

$\frac{A}{6}=a$

Let side of Big cube = 6 unit

$\therefore$ side of small cube = 1 unit.

$\therefore$ zero side printed $\Rightarrow (n-2{)}^3$

$=(6-2{)}^2$

$=4^3=64$

option C