For the same cross-sectional area and for a given load, the ratio of depressions for the beam of a square cross-section and circular crosssection is

$\delta =\frac{W{\mathcal{l}}^3}{3YI}$, where W = load, $\mathcal{l}=$length of beam and I is geometrical moment of inertia for rectangular beam,

$\mathrm{I}=\frac{{\mathrm{bd}}^3}{12}$where b = breadth and d = depth
For square beam b = d

For a beam of circular cross-section,${\mathrm{I}}_2=\left(\frac{{\mathrm{\pi r}}^4}{4}\right)$

($\because b^2={\mathrm{\pi r}}^2$ i.e., they have same cross-sectional area)