Question

Three cubes whose edges are $3$ cm, $4$ cm and $5$ cm respectively are melted without any loss of metal into a single cube. The edge of the new cube is ___________.

• A. $6$ cm
• B. $12$ cm
• C. $9$ cm
• D. $10$ cm

Answer 1

Answer: (A)

$6$ cm

Given,

cube 1 : edge $=3$ cm

Volume of cube 1 $=3^3=27cc$

cube 2 : edge $=4$ cm

Volume of cube 2 $=4^3=64cc$

cube 3 : edge $=5$ cm

Volume of cube 3 $=5^3=125cc$

Total volume $=27+64+125=216cc$

Volume of new cube with side $a=a^3$

$\Rightarrow a^3=216$

$\Rightarrow a=\sqrt[3]{3216}=6$ cm.

Therefore, side of new cube $=6$ cm

Option (A) is correct