Question

If the radius of a sphere is increased by 2 cm, then its surface area increases by 352 cm^2 . The radius of the sphere before the increase was:

Answer 1

Let the radius of sphere be r cm

Then by question,

4Π(r+2)2−4Πr2=352

4Π{(r+2)2−r2}=352

4Π{r2+4+4r−r2}=352

Π(1+r)=35216=22

r= 6cm

Answer 2

The radius of the sphere before the increase was 6 cm.

Let the radius of a sphere be 'r' cm

We know, surface area of a sphere of radius 'r' is given as 4×П×r²  cm²

Similarly, for a sphere of radius of (r+2) cm, its surface area should be :

4×П×(r+2)²  cm²

Now, according to the question, the difference between their surface area is 352 cm²

So, [4×П×(r+2)² - 4×П×r²] = 352

⇒4×П[(r+2)² - r²] = 352

⇒ П[ (r²+4+4r) - r²] = 88                   [Expanding like (a+b)² = a² + b² + 2ab]

⇒ П(4 + 4r) = 88

⇒ 4П(1 + r) = 88

⇒ П(1 + r) = 22

⇒ (22÷7) × (1 + r) = 22                       [As we know П = 22÷7]

⇒ (1 + r) ÷ 7 = 1

⇒ (1 + r) = 7

⇒ r = 7 - 1

⇒ r = 6cm

So, the radius 'r' of the sphere is 6cm.