Question

If the edge of a cube is increased by 4 cm, the surface area will increase by 432 cm². Then the original length of each edge of the cube is _____.
1. 8 cm
2. 7 cm
3. 6 cm
4. 9 cm

Answer 1

Correct Answer - Option 2 : 7 cm

Given:

The edge of the cube increased by 4cm.

Increase in surface area = 432 cm²

Formula used:

Total surface area of cube = 6a²

Where a is the side of the cube

Calculation:

Increased surface area = 6 × (a + 4)² = 6a² + 432

⇒ 6 × (a² + 8a + 16) = 6a² + 432

⇒ a² + 8a + 16 = a² + 72

⇒ 8a = 56

⇒ a = 7 cm

∴ The original length of each edge of the cube is 7 cm.