Let $n\ge 2$, and let $r,R\in\mathbb R$ satisfy $r>0$ and $R>0$. Equip $\mathbb R^{2n}$, with coordinates $(q_1,p_1,\dots,q_n,p_n)$, with the standard symplectic form $\omega_0=\sum_{i=1}^n dq_i\wedge dp_i$. Define $B^{2n}(r)=\{x\in\mathbb R^{2n}: |x|<r\}$ and $Z^{2n}(R)=\{(q_1,p_1,\dots,q_n,p_n)\in\mathbb R^{2n}: q_1^2+p_1^2<R^2\}$. Then there exists a smooth embedding $\varphi:B^{2n}(r)\to Z^{2n}(R)$ such that $\varphi^*(\omega_0|_{Z^{2n}(R)})=\omega_0|_{B^{2n}(r)}$ if and only if $r\le R$.