Three cubes of a metal whose edges are 3, 4 and 5 cm respectively are melted and formed into a single cube. If there is no loss of metal in the process, find the side of the new cube.

Correct option is C

Given:

Sides of metal cubes = 3cm, 4cm, 5cm 

Side of the new cube = ?

Formula Used:

The volume V of a cube is given by the formula:

​$$V = \text{(side)}^3$$ 

Solution: 

Let the side length of the new cube be sss.

For the cube with side 3 cm:

​$$V_1 = 3^3 = 27 \, \text{cm}^3$$​​

For the cube with side 4 cm:

​$$V_2 = 4^3 = 64 \, \text{cm}^3$$​​

For the cube with side 5 cm:

​$$V_3 = 5^3 = 125 \, \text{cm}^3$$ 

​The total volume of the metal is the sum of the volumes of the three cubes:

​$$V_{\text{total}} = V_1 + V_2 + V_3 = 27 + 64 + 125 = 216 \, \text{cm}^3$$ 

The volume of the new cube will be equal to the total volume of the metal. So:

​$$s^3 = 216$$​​

$$s = \sqrt[3]{216} = 6 \, \text{cm}$$ 

The side of the new cube is 6 cm.