Hy-Spherical

We can plot out these 2 spheres on the Cartesian plane with equations $x^2 + y^2 = R^2$ and $(x-R)^2 + y^2 = R^2$ .

It's obvious that the $x$ -coordinate of the intersecting points of these 2 spheres is $\tfrac R2$ .

Let $V$ denote the volume in question, then by volume of revolution, $\begin{aligned} \dfrac V2 &=& (\text{volume of one sphere of radius } R) - (\text{half the volume of the intersecting regions}) \\ &=& \frac43 \pi R^3 - \pi \int_{R/2}^R y^2 \, dx \\ &=& \frac43 \pi R^3 - \pi \int_{R/2}^R (R^2 - x^2) \, dx \\ &=& \frac43 \pi R^3 - \frac5{24} \pi R^3 = \frac98 \pi R^3 \\ V &=& \frac94 \pi R^3. \end{aligned}$

The answer is $\frac94 = \boxed{2.25}$ .