  Let $\mathcal{O}(\mbox{Spin}_{q^{1/2}}(2n+1))$ and $\mathcal{O}(SO_q(2n+1))$
be the quantized algebras of regular functions on the Lie groups
$\mbox{Spin}(2n+1)$ and $SO(2n+1)$, respectively. In this article, we prove
that the Gelfand-Kirillov dimension of a simple unitarizable
$\mathcal{O}(\mbox{Spin}_{q^{1/2}}(2n+1))$-module $V_{t,w}^{\mbox{Spin}}$ is
the same as the length of the Weyl word $w$. We show that the same result holds
for the $\mathcal{O}(SO_q(2n+1))$-module $V_{t,w}$, which is obtained from
$V_{t,w}^{\mbox{Spin}}$ by restricting the algebra action to the subalgebra
$\mathcal{O}(SO_q(2n+1))$ of $\mathcal{O}(\mbox{Spin}_{q^{1/2}}(2n+1))$.
Moreover, we consider the quantized algebras of regular functions on certain
homogeneous spaces of $SO(2n+1)$ and $\mbox{Spin}(2n+1)$ and show that its
Gelfand-Kirillov dimension is equal to the dimension of the homogeneous space
as a real differentiable manifold.
