# 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?

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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

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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,

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