Question

If the radius of a sphere is increased by $5cm,$ then its surface area increases by 704${cm}^2$ . Theradius of the sphere before the increase was:

• A. 2.1 cm
• B. 3.1 cm
• C. 4.1 cm
• D. 5.1 cm

Answer 1

The correct option is B 3.1 cm

S.A. after increase = S.A. before increase + 704 cm²

⇒ 4π(r + 5)² = 4πr² + 704

⇒ 4π(r² + 10rπ + 25) = 4πr² + 704

⇒ 4πr² + 40πr + 100π = 4πr² + 704

⇒ 40πr + 100π = 704

⇒ 22/7 × (40r + 100) = 704

⇒ 40r + 100 = 224

⇒ 40r = 124

⇒ r = 3.1 cm

So, initial radius of sphere = 3.1 cm