Question

Three solid cubes of edges 4 cm, 9 cm, and 10 cm are melted together to make a new cube. If 793 cm³ of the melted material is lost due to improper handling. What is the total surface area of the newly formed cube?
1. 864 cm²
2. 600 cm²
3. 660 cm²
4. 750 cm²

Answer 1

Correct Answer - Option 2 : 600 cm²

The total volume of 3 cubes = 4³ + 9³ + 10³

⇒ 64 + 729 + 1000

⇒ 1793

∵ 793 cm³ of the melted material is lost due to improper handling.

∴ The volume of the newly formed cube = (1793 – 793) = 1000 cm³

Let the side of the newly formed cube is x cm

⇒ x³ = 1000

⇒ x = (1000)^1/3

⇒ x = 10 cm

Thus, the total surface area of the newly formed cube = 6 × x²

= 6 × (10)² = 6 × 100 = 600 cm²