Question

A $5\times 5\times 5$ cube is formed by using $1\times 1\times 1$ cubes. If we add another layer of such $1\times 1\times 1$ cube around the $5\times 5\times 5$ cube. What will be the number of $1\times 1\times 1$ cubes in the newly formed cube?

• A. $216$
• B. $343$
• C. $294$
• D. $264$

Answer 1

The correct option is B $343$

A $5\times 5\times 5$ cube has $5$ cubes of $1\times 1\times 1$ cubes along its length, breadth and width each. If we add a layer of $1\times 1\times 1$ cubes (the smaller cubes) then the new cube will have following dimensions:
Length $=5+1+1=7$; breadth $=5+1+1=7$ and width $=5+1+1=7$.
So the number of $1\times 1\times 1$ cubes in this $7\times 7\times 7$ cube
$=7\times 7\times 7=343$.