Question

Three metal cubes whose edges measure $3cm,4cm$ and $5cm$ respectively are melted to form a single cube. Find its edge. Also, find the surface area of the new cube.

• A. $6cm$; $216{cm}^2$
• B. $6cm$; $126{cm}^2$
• C. $6cm$; $106{cm}^2$
• D. $5cm$; $216{cm}^2$

Answer 1

The correct option is A $6cm$; $216{cm}^2$

Volume of resulting metal cube $=$ Volume of metal cube $1+$ Volume of metal cube $2+$ Volume of metal cube $3$
Volume of a cube $=a^3$
Let side of the resulting cube be $A$.

So, $A^3=3^3+4^3+5^3$
$=>A^3=27+64+125$
$=>A^3=216$
$=>A=6$
Hence, length of side of the resulting metal cube is $6cm$.

Total surface area of a cube $=6a^2$
$=6\times 6^2=216{cm}^2$