Question

Three cubes whose edges are 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. Find the surface area of the new cube.

• A. $210c{m}^2$
• B. $213c{m}^2$
• C. $224c{m}^2$
• D. $216c{m}^2$

Answer 1

The correct option is D $216c{m}^2$

Sum of volume of all the cubes melted will be equal to the volume of the new cube formed.

Let x be the edge of the new cube.
Hence,
$x^3=3^3+4^3+5^3$
$=27+64+125=216=6^3$

$\Rightarrow x=6cm$

Now, surface area of the new cube
$=6\times (edge{)}^2=6\times 6^2=216c{m}^2$