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 $π =\frac{22}{7}$)
Answer & explanation
Correct answer: option 4
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.