A 9 cm solid metallic cube and a solid metallic cuboid having dimensions 5 cm, 13 cm, 31 cm are melted and recast into a single cube. What is the total surface area (in cm²)of the new cube?

1176

We know that,

Side of cube = 9 cm

We have,

Length = 5 cm

breadth = 13 cm

height = 31 cm

Volume of Solid metallic cube = 9³ = 729 cm³

Volume of Solid metallic cuboid = 5 × 13 × 31 = 2015 cm³

Volume cube = Volume of Solid metallic cube + Volume of Solid metallic cuboid= 729 + 2015 = 2744 cm³

Side of cube = (a)³ = 2744

a = 14 cm

Total surface area of cube = 6 × 14 × 14 = 1176 cm²