Question

Three mental cubes of volume $125c{m}^3$, $64c{m}^3$ and $27c{m}^3$ are melted to form a new cube, then the edge of the new cube formed is:

• A. $12cm$
• B. $6cm$
• C. $20cm$
• D. $10cm$

Answer 1

Answer: (B)

$6cm$

Given, $V_1=125c{m}^3$, $V_2=64c{m}^3$, and $V_3=27c{m}^3$.

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

Then, the volume of the new cube $V=V_1+V_2+V_3$

$=125+64+27=216c{m}^3$.

Suppose $a$ is the required edge.

Then, volume $V=a^3=216c{m}^3$.

$\therefore$ Edge of new cube $=\sqrt[3]{3216}=6cm$.

Hence, option $B$ is correct.