Question

If the radius of a sphere is increased by 4 cm, its surface area increases by 704 cm². What is the radius of the sphere before the change?
1. 5 cm
2. 8 cm
3. 12 cm
4. 6 cm

Answer 1

Correct Answer - Option 1 : 5 cm

Given:

Radius increased by = 4 cm 

Difference between increased surface area and initial surface area of the sphere = 704 cm²

Formula used,

Area of the sphere = 4πr²

Where,

r → Radius of sphere

Calculation

Area of the sphere = 4πr2

According to the question, 

4π(r + 4)² – 4πr² = 704 

⇒ 4 × 22/7 × [(r + 4)² - r²] = 704

⇒ (r + 4)² - r² = 56

⇒ r² + 16 + 8r - r² = 56

⇒ 8r = 40

⇒ r = 5 

∴ The radius = 5 cm