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

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 

\( - \frac{{\Delta r}}{r} = \frac{p}{{3B}}\)