# What is the edge of the third smaller cube?

A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, find the edge of the third smaller cube?

- 8 cm
- 10 cm
- 12 cm
- None of these

**Answer: (2) 10 cm **

**Explanation:-**

The age of a metal cube =12 cm

Therefore the volume of the cube = 12 x 12 x 12

= 1728 cm ^3

The age of first smaller cube = 6 cm

Therefore, the volume of the cube = 6 x 6 x 6

= 216 cm^3

The age of second smaller cube = 8 cm

Therefore, the volume of the cube = 8 x 8 x 8

= 512 cm cube

So, the volume of the third smaller cube = 1728 – (216 + 512)

= 1728 – 728

= 1000 cm^3

Thus, the age of the third smaller cube = cube root of (1000)

= 10 cm

Then, the age of the third smaller cube is 10 cm.

Hence, the correct answer is option (2) 10 cm.