Question

A cube of lead with edges measuring $6$ cm each is melted and formed into $27$ equal cubes. What will be length of the edges of the new cubes?

• A. $3$ cm
• B. $4$ cm
• C. $2$ cm
• D. $1.5$ cm

Answer 1

The correct option is C $2$ cm

Let the edge of the small cubes $=x$ cm.

Then, Volume of larger cube $=27\times \text{Volume of small cubes}$.

$\Rightarrow (6{)}^3=27\times (x{)}^3\Rightarrow \frac{216}{27}=x^3$

$\Rightarrow x^3=8$ $\Rightarrow x=\sqrt[3]{38}=2cm$.

Hence, option $C$ is correct.