$B = \frac{{ - pV}}{{\Delta V}}$                                    $...(i)$

The volume of a spherical object of radius $r$ is given as

$V = \frac{4}{3}\pi {r^3}\,\,,\,\,\Delta V = \frac{4}{3}\pi \left( {3{r^2}} \right)\Delta r$

$\therefore  - \frac{V}{{\Delta V}} = \frac{{\frac{4}{3}\pi {r^3}}}{{\frac{4}{3}\pi 3{r^2}\Delta r}}\,\,or\,\, - \frac{V}{{\Delta V}} =  - \frac{r}{{3\Delta r}}$

Put this value in eqn. $(i)$, we get

$B =  - \frac{{pr}}{{3\Delta r}}$

Fractional decrease in radius is 

$ - \frac{{\Delta r}}{r} = \frac{p}{{3B}}$