A solid metallic cube of side 9 cm and solid metallic cuboid having dimensions 5 cm, 13 cm, 31 cm are melted to form single cube. How much(in ₹) is the cost to polish the new cube at a rate of ₹10 per cm²?

11,760

We know that,

Volume of cube = (side)³

Volume of cuboid = length × breadth × height

Total surface area of cube = 6 × side²

We have,

Side of cube = 9 cm

Length of the Cuboid  = 5 cm, breadth = 13 cm, height = 31 cm

Volume of Solid metallic cube = (9)³ = 729 cm³

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

Volume of single cube = Volume of Solid metallic cube + Volume of Solid metallic cuboid

= 729 + 2015 = 2744 cm³

Side of Recasted cube = (Side)³ = 2744

= side = 14 cm

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