The radius of a circle is decreased by 30%. Then by what percent will the circumference be decreased?

Let the initial radius of the circle be' r units'.

Given that the radius of a circle is decreased by 30%.

Thus, the new radius = (r - 30% of r)

$=\mathrm{r}-\frac{30}{100}\mathrm{r}$ units

$=\frac{(100-30)\mathrm{r}}{100}$ units

$=\frac{7\mathrm{r}}{10}$ units

Now, Original circumference = $2\mathrm{\pi r}$ units

And, new circumference$=2\mathrm{\pi }\frac{7}{10}=\frac{7\mathrm{\pi }}{5}$ units

Thus, 

Required percentage change$=\frac{\mathrm{Difference} \mathrm{in} \mathrm{circumference}}{\mathrm{Original} \mathrm{circumference}}\times 100 \%$

$=\frac{2\mathrm{\pi r}-{\displaystyle \frac{7}{5}}\mathrm{\pi r}}{2\mathrm{\pi r}}\times 100\%$

$=\frac{10\mathrm{\pi r}-{\displaystyle 7}\mathrm{\pi r}}{5\times 2\mathrm{\pi r}}\times 100\%$

$=\frac{3\mathrm{\pi r}}{10\mathrm{\pi r}}\times 100\%$

$=30\%$

Hence, the circumference will also decrease by 30%.