Question

the diaoeter of a sphere is decreses by 25 present . by what present its curve surface area decreses?

Answer 1

Let, the radius of sphere = r

Then, curved surface area of sphere

$4\pi {r}^{2}$
After increasing 25% in radius :

$\frac{5r}{4}$

Now, curved surface area of sphere :

$4\pi { (\frac{5r}{4} )}^{2} \\ \\ = > \frac{25}{4} \pi {r}^{2}$

Now, change in area :

$\frac{ \frac{25}{4}\pi {r}^{2} - 4\pi {r}^{2} }{4\pi {r}^{2} } \times 100 \\ \\ = > \frac{ \frac{9}{4}\pi {r}^{2} }{4\pi {r}^{2} } \times 100 \\ \\ = > \frac{9}{16} \times 100 \\ \\ = > 56.25$

So, the increasing in area will be 56.25%