Three cuboids of dimensions 5 cm × 6 cm × 7cm, 4cm × 7cm × 8 cm and 2 cm × 3 cm × 13 cm are melted and a cube is made. Find the side of cube.

#### Solution

\[\text { The dimensions of the three cuboids are 5 cm }\times 6 cm \times 7 cm, 4 cm \times 7 cm \times 8 cm \text { and } 2 cm \times 3 cm \times 13 cm . \]

\[\text { Now, a new cube is formed by melting the given cuboids }. \]

\[ \therefore \text { Voulume of the cube = sum of the volumes of the cuboids }\]

\[ = (5 cm \times 6 cm \times 7 cm) + (4 cm \times 7 cm \times 8 cm) + (2 cm \times 3 cm \times 13 cm)\]

\[ = (210 {cm}^3 ) + (224 {cm}^3 ) + (78 {cm}^3 )\]

\[ = 512 {cm}^3 \]

\[\text { Since volume of a cube = (side ) }^3 , \text { we have }: \]

\[512 =\text { (side ) }^3 \]

\[ \Rightarrow (\text { side) } = \sqrt[3]{512} = 8 cm\]

\[ \therefore \text { The side of the new cube is 8 cm } .\]