Question

Three solid spheres of radius 3 cm, 4 cm and 5 cm are melted and recasted into a solid sphere. What will be the percentage decrease in the surface area?
1. 14 percent
2. 12 percent
3. 16 percent
4. 28 percent

Answer 1

Correct Answer - Option 4 : 28 percent

Given:

Three spheres of radius 3 cm, 4 cm, and 5 cm

Concept:

The volume of the sphere = (4/3) × π × R³, Where R is the radius of the sphere

Calculation:

Let be assume the radius of the recast sphere is R

⇒ (4/3) × π × R³ = (4/3) × π × (3³ + 4³ + 5³)

⇒ R = 6 cm

⇒ The total surface of sphere = 4 × π × R²

⇒ The total surface area of all three-sphere = 4 × π × (3² + 4² + 5²) = 200π 

⇒ The total surface area of recast sphere = 4 × π × R² = 4 × π × 6² = 144π 

⇒ Percentage decrease in surface area = (200π - 144π)/200π × (100) = 28%

∴ The required result will be 28%.