Question

From a $10\times 10\times 10$ cube, which is formed by combination of $1\times 1\times 1$ cubes, a layer of the smaller cubes is removed. What will be the number of $1\times 1\times 1$ cubes present in this new cube?

• A. $900$
• B. $488$
• C. $512$
• D. $729$

Answer 1

Answer: (C)

$512$

A $10\times 10\times 10$ cube has 10 cubes of $1\times 1\times 1$ cubes along it length, breadth and width each. If we remove a layer of $1\times 1\times 1$ cubes (the smaller cubes) then the new cube will have following dimensions:
$length=10-1-1=8;breadth=10-1-1=8$ and $width=10-1-1=8$.
So the number of $1\times 1\times 1$ cubes in this $8\times 8\times 8cube$
$=8\times 8\times 8\times =512$.Hence option C is correct.