Question

From a $10\times 10\times 10$ cube which is formed by combinations 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

The correct option is C $512$

A $10\times 10\times 10$ cube has 10 cubes of$1\times 1\times 1$cubes along its 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 dimension :
lngth$=10-1-1=8;$ breadth$=10-1-1=8;$ and width$=10-1-1=8$.
So the number of $1\times 1\times 1$ cubes in this $=8\times 8\times 8=512$