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 in the $5\times 5\times 5$ cube, the 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

Answer: (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 $=7\times 7\times 7=343$