Question

The diameter of a sphere is decreased by $20\%$ .By what percent does it curved surface area decrease.

Answer 1

Let the original diameter be $d$ units.

Therefore, original radius will be $\frac{r}{2}$ units

Since, diameter of a sphere is decreased by $20\%$, therefore, radius of the sphere is also decreased by $20\%$.

Hence, new radius $R=\frac{r}{2}-0.2\times \frac{r}{2}=0.4r$

Original CSA of sphere $=4\pi (\frac{r}{2}{)}^2=\pi r^2$

Now, new CSA of sphere $=4\pi R^2$

$=4\pi (0.4r{)}^2$

$=0.64\pi r^2$

Decrease percent in CSA $=\frac{\pi r^2-0.64\pi r^2}{\pi r^2}\times 100\%=36\%$