Question

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?
1. 1362
2. 865
3. 2744
4. 1176

Answer 1

Correct Answer - Option 4 : 1176

Given:

Side of cube = 9 cm

Cuboid Dimensions

Length = 5 cm, breadth = 13 cm, height = 31 cm

Formula used:

Volume of cube = (side)³

Volume of cuboid = length × breadth × height

Total surface area of cube = 6 × side²

Calculation:

Volume of Solid metallic cube

⇒ 9³

⇒ 729 cm³

Volume of Solid metallic cuboid

⇒ 5 × 13 × 31

⇒ 2015 cm³

Volume of Recast single cube

⇒ Volume of Solid metallic cube + Volume of Solid metallic cuboid

⇒ 729 + 2015

⇒ 2744 cm3

Side of Recast cube

⇒ (Side)³ = 2744

⇒ side = 14 cm

Total surface area of cube

⇒ 6 × 14 × 14

⇒ 1176 cm²

∴ The total surface area of recast cube is 1176 cm².