Volume of sphere=(4/3)πr^3 where r=radius. Volume of hemisphere is (2/3)πr^3.
Surface area of sphere is 4πr^2 and that of hemisphere is 2πr^2+πr^2=3πr^2, that is, the area of the flat circular base and the curved surface.
H=radius of hemisphere, S=radius of sphere, so 4πS^2=3πH^2, and 4S^2=3H^2, or S=H√3/2.
Note that √3 cubed is 3√3.
Volume of sphere=(4/3)πS^3, volume of hemisphere=(2/3)πH^3, ratio of volumes is sphere/hemisphere=2S^3/H^3=2H^3*3√3/8H^3=6√3/8=1.3 approx.