Question

A wax cube of edge $6cm$ is melted and formed into three smaller cubes. If the edges of two smaller cubes are $3cm$ and $4cm$, what is the edge of the third smaller cube?

• A. $2cm$
  
• B. $3cm$
  
• C. $5cm$
  
• D. $7cm$
  

Answer 1

The correct option is C $5cm$

We know, volume of the cube $V=a^3$, where $a$ is the edge of the cube.

Let the edge of the third cube be $a$ cm.

Then,

$\Rightarrow a^3+3^3+4^3=6^3$

$\Rightarrow a^3+27+64=216$
$\Rightarrow a^3=125$

$\Rightarrow a=\sqrt[3]{3125}=5cm$.

Hence, option $C$ is correct.