Question

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

Answer 1

Let the edge of the third cube be x cm .

Three small cubes are formed by melting the cube of edge 12 cm . 

Edges of two small cubes are 6 cm and 8 cm . 

\[\text { Now, volume of a cube = (side ) }^3 \]

\[\text { Volume of the big cube = sum of the volumes of the three small cubes }\]

\[ \Rightarrow (12 )^3 = (6 )^3 + (8 )^3 + (x )^3 \]

\[ \Rightarrow 1728 = 216 + 512 + x^3 \]

\[ \Rightarrow x^3 = 1728 - 728 = 1000\]

\[ \Rightarrow x = \sqrt[3]{1000} = 10 cm\]

\[ \therefore \text { The edge of the third cube is 10 cm } .\]