Question : If the radius of a sphere is increased by 2 cm, then its surface area increases by 352 cm2. The radius of the sphere initially was: (use $\pi =\frac{22}{7}$)
Option 1: 4 cm
Option 2: 5 cm
Option 3: 3 cm
Option 4: 6 cm
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Correct Answer: 6 cm
Solution :
Let the initial radius be $r$
Area before increment $= 4\pi r^2$
Given: After increasing the radius by 2 cm, the area is increased by = 352 cm$^2$
According to the question,
$4\pi r^2 + 352 = 4\pi (r+2)^2$
⇒ $4\pi r^2 + 352 = 4\pi (r^2+4r+4)$
⇒ $4\pi r^2 + 352 = 4\pi r^2+16\pi r+16\pi$
⇒ $352 = 16\pi(1+r)$
⇒ $\frac{352}{16\pi} = 1+r$
⇒ $\frac{352×7}{16×22} = 1+r$
⇒ $7 = 1+r$
⇒ $r = 6$ cm
Hence, the correct answer is 6 cm.
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