Question

If 1" and 2" cubes are one each in number, what will be the total number of $\frac{1}{2}$ cubes?

• A. 510
• B. 440
• C. 424
• D. 460
• E. 540

Answer 1

The correct option is B 440

Cube of 2" dimension = 1
Cube of 1" dimension = 1
Let the cube of dimension $\frac{1}{2}$" = $x$
Equating the volume of bigger cube with that of smaller cubes
$4\times 4\times 4=1\times 1\times 1+x\times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}+2\times 2\times 2$
$64=1+\frac{x}{8}+8$
$55=\frac{x}{8}$
$x=55\times 8$
$x=440$
Thus there will be 440 small cubes of dimension $\frac{1}{2}$"