3D positively curved space

Question

If we consider 2D euclidean surface consists of infinite concentric circles and 3D euclidean surface consists of infinite concentric spheres. If 2D surface is positively curved the radius of the circles at a distance $r$ from the origin becomes $R \sin(\frac{r}{R})$, where $R$ is the radius of the 2-Sphere. Similarly for 3D positively curved space the radius of the spheres at a distance $r$ from the origin becomes $R \sin(\frac{r}{R})$,in this case whether $R$ is the radius of the 3-spheres?

Answer 1

For 3-Sphere the radius of the Curvature is R. For more information look this Cosmology Mathematical Tripos

If you look the equations 1.1.5 and 1.1.14 that you ll see that the author defined a is the radius of the 3-sphere as "a" and used it to desribe the metric.