Let $B_{R_1} \subseteq \mathbb{R}^3$ be the ball of radius $R_1 > 0$ centred at the origin. Let $C_{R_2,d}$ the solid cylinder with radius $R_2 > 0$ and with axis at distance $d$ from the origin. For instance $$ C_{R_2, d} = \{(x, y, z) \in \mathbb{R}^3 : (x - d)^2 + y^2 \le R_2^2\}. $$
Is there a formula to compute the volume of $B_{R_1} \cap C_{R_2, d}$ as function of $R_1, R_2, d$?