The bulk modulus of a spherical object is B. If it is subjected to uniform pressure p, the fractional decrease in radius is 

The object is spherical and the bulk modulus is represented by B. It is the ratio of normal stress to the volumetric strain.
Hence, $\mathrm{B}=\frac{\mathrm{F}/\mathrm{A}}{\mathrm{\Delta V}/\mathrm{V}}\left(\because \mathrm{p}=\frac{\mathrm{F}}{\mathrm{A}}\right)$
$\Rightarrow \frac{\mathrm{\Delta V}}{\mathrm{V}}=\frac{\mathrm{p}}{\mathrm{B}}=\left|\frac{\mathrm{\Delta V}}{\mathrm{V}}\right|=\frac{\mathrm{p}}{\mathrm{B}}$
Here, p is applied pressure on the object and $\frac{\mathrm{\Delta V}}{\mathrm{V}}$is volume strain. 
Fractional decrease in volume, $\frac{\mathrm{\Delta V}}{\mathrm{V}}=3\frac{\mathrm{\Delta R}}{\mathrm{R}}\left(\because \mathrm{V}=\frac{4}{3}{\mathrm{\pi R}}^3\right)$
Volume of the sphere decreases due to the decrease in its radius, hence$\frac{\mathrm{\Delta V}}{\mathrm{V}}=\frac{3\mathrm{\Delta R}}{\mathrm{R}}=\frac{\mathrm{P}}{\mathrm{B}}\Rightarrow \frac{\mathrm{\Delta R}}{\mathrm{R}}=\frac{\mathrm{P}}{3\mathrm{B}}$