Question

If three cubes of metal whose edges are $30$ cm, $40$ cm and $50$ cm respectively are melted and formed into a single cube, the total surface area of the single new cube is

• A. $2.0m^2$
• B. $2.15m^2$
• C. $2.16m^2$
• D. $2.2m^2$

Answer 1

Answer: (C)

$2.16m^2$

Let the side of single new cube be $a$.
Then $a^3={30}^3+{40}^3+{50}^3$
$={10}^3(27+64+125)$
$={10}^3\times 6^3$
$\therefore a=60$ cm
Total surface area of new cube $=6a^2=6\times {60}^2$
$=21600c{m}^2$, i.e. $2.16$ $m^2$