Question

The side of a solid metallic cube is $50\text{cm}$. it is melted and recast into $8000$ similar solid cubical dies. Find the side of each die.

• A. $2.5\text{cm}$
• B. $6\text{cm}$
• C. $1.9\text{cm}$
• D. $5.2\text{cm}$

Answer 1

The correct option is A $2.5\text{cm}$

According to the statement,

Volume of big cube $=8000\times$ Volume of small cube.

Let $x$ be the side of small cube,

$(50{)}^3=8000(x^3)$

$x^3=\frac{125000}{8000}$

$⟹x=\frac{50}{20}=2.5\text{cm}$

Hence, the length of side of each small die will be $2.5\text{cm}$.