Two spheres

The volume is proportional to $r^3$ and the surface are is proportional to $r^2$ . So the ratio of the volume to the surface area will be proportional to $r^{3/2}$ , and $3^{3/2} = \boxed{5.196}$

Let the radius of the larger sphere be $R$ and that of the smaller sphere be $r$ .
So, ratio of surface areas = $\dfrac{4 × \pi × R^2}{4 × \pi × r^2} = \dfrac{3}{1}\\ \\ {\dfrac{\cancel{4} × \cancel{\pi} × R^2}{\cancel{4} × \cancel{\pi} × r^2}} = \dfrac{3}{1}\\ \\ {\left(\dfrac{R}{r}\right)}^{2} = \dfrac{3}{1}\\ \\ \dfrac{R}{r} = \sqrt{\dfrac{3}{1}} \longrightarrow \boxed{1}$

Ratio of volumes = $\dfrac{4 × \pi × R^3 × 3}{3 × 4 × \pi × r^3} = \dfrac{N}{1}\\ \\ {\dfrac{\cancel{4} × \cancel{\pi} × R^3 × \cancel{3}}{\cancel{3} × \cancel{4} × \cancel{\pi} × r^3}} = \dfrac{N}{1}\\ \\ {\left(\dfrac{R}{r}\right)}^{3} = \dfrac{N}{1}\\ \dfrac{R}{r} = \sqrt[3]{\dfrac{N}{1}} \longrightarrow \boxed{2}$

From $\boxed{1}$ and $\boxed{2}$ , we get:-
$\sqrt{3}{1} = \sqrt[3]{\dfrac{N}{1}}$
Cubing on both sides, we get:-
$\dfrac{{\sqrt{3}}^3}{{\sqrt{1}}^3} = \dfrac{N}{1}\\ N = {\left(\sqrt{3}\right)}^3\\ N = 3\sqrt{3}\\ N = \color{#69047E}{\boxed{5.196}}$