  We consider Bernoulli first-passage percolation on the $d$-dimensional
hypercubic lattice with $d \geq 2$. The passage time of edge $e$ is $0$ with
probability $p$ and $1$ with probability $1-p$, independently of each other.
Let $p_c$ be the critical probability for percolation of edges with passage
time $0$. When $0\leq p<p_c$, there exists a nonrandom, nonempty compact convex
set $\mathcal{B}_p$ such that the set of vertices to which the first-passage
time from the origin is within $t$ is well-approximated by $t\mathcal{B}_p$ for
all large $t$, with probability one. The aim of this paper is to prove that for
$0\leq p<q<p_c$, the Hausdorff distance between $\mathcal{B}_p$ and
$\mathcal{B}_q$ grows linearly in $q-p$. Moreover, we mention that the approach
taken in the paper provides a lower bound for the expected size of the
intersection of geodesics, that gives a nontrivial consequence for the
\textit{critical} case.
