Question : 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 $\pi=22 / 7$ )
Option 1: 8.2 cm
Option 2: 6.8 cm
Option 3: 5.2 cm
Option 4: 6.2 cm
Correct Answer: 6.2 cm
Solution :
Let the radius of the sphere be $r$ cm = 4$\pi r^{2}$.
New radius = $r + 5$
According to the question,
4$\pi (r + 5)^{2}$ = 704
⇒ 4$\pi[(r + 5)^{2} - r^{2}$] = 704
⇒ 4 × $\frac{22}{7}[r^{2} + 25 + 10r - r^{2}]$ = 704
⇒ $25 + 10r = 704 × \frac{7}{22} × \frac{1}{4}$ = 25 + 10$r$ = 56
⇒ 10$r$ = 56 – 25 = 31
⇒ $r = \frac{31}{10}$ = 3.1
So, The diameter of the sphere = 2 × 3.1 = 6.2
Hence, the correct answer is 6.2 cm.
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