= Solution
Assume spherical bodies of common <mass density> $\rho$, a well-mixed belt, and that $n(D)dD$ counts bodies in the entire belt rather than per unit volume. A body of diameter $D$ has mass $\pi\rho D^3/6$. The <mass normalization of a power-law size distribution> is
$$
M_{\rm tot}=\frac{\pi\rho K}{6}\int_{D_{\min}}^{D_{\max}}D^{3-\alpha}\,dD.
$$
Consequently
$$
\boxed{K=\frac{6M_{\rm tot}}{\pi\rho}
\begin{cases}
\displaystyle\frac{4-\alpha}{D_{\max}^{4-\alpha}-D_{\min}^{4-\alpha}},&\alpha\ne4,\\
\displaystyle\frac1{\log(D_{\max}/D_{\min})},&\alpha=4.
\end{cases}}
$$
The thin-torus volume is circumference times radial width times full vertical height,
$$
V\simeq(2\pi r)\,dr\,(2I_{\max}r)=4\pi I_{\max}r^2dr.
$$
The local number-density distribution needed for a <planetesimal collision rate> is $n(D)/V$. Thus belt geometry does not enter this total-number $K$ but does enter collision rates. This approximation treats the stated height as uniform, independent of size.
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