# Three metal cubes whose edges measure 3cm, 4cm and Scm respectively are melted to form a single cube, find its :

- 15 cm
- 12 cm
- 6 cm
- none of these

**Answer: (3) 6 cm **

**Explanation:-**

The edge of first cube = 3 cm

Then, volume of first cube (V_{1} ) = 3^3 = 3 x 3 x 3

= 27 cm^3

The of second cube = 4 cm

Then, volume of second cube(V_{2}) = 4^3 = 4 x 4 x 4

= 64 cm^3

The edge of third cube = 5 cm

Then, volume of third cube(V_{3}) = 5^3 = 5 x 5 x 5

= 125 cm^3

After melting, volume of the ‘single’ new cube is V cm^{3}.

Let the edge of the new cube be x cm.

The sum of the volume of the three cubes before melting = Volume of the new cube formed after melting

V_{1} + V_{2} + V_{3} = V

27 + 64 + 125 = (x)^{3 } x^{3} = 216 x = ^{3} = 6 cm

The required edge (of the new cube) is 6 cm.

Hence, the correct answer is option (3) 6 cm