When the radius of a sphere is increased by 5 cm, its surface area increases by 704 cm². The diameter of the original sphere, is (Take $π =\frac{22}{7}$)

6.2 cm

We know that,

The surface area of sphere = 4πr²

Given in the question,

The radius of a sphere is increased by 5 cm

Surface area increased by 704 cm²

Let radius of sphere be r cm

New radius of sphere = r + 5

According to the question

4 π (r + 5)² – 4 πr² = 704

= 4 π [(r + 5)² – r²] = 704

= 4 × \(\frac{22}{7}\) [r² + 25 + 10r – r²] = 704

= 25 + 10r = 704 × \(\frac{7}{22}\) × \(\frac{1}{4}\)

= 25 + 10r = 56

= 10r = 56 – 25 = 31

= r = 3.1

The diameter of sphere = 2 × 3.1 = 6.2 cm.