The nuclear density (\(\rho\)) is approximately constant for all nuclei, independent of their atomic or mass numbers. This constancy is due to the direct proportionality between nuclear mass and volume with the mass number (\(A\)).
1. Nuclear Density for \(^{40}\text{Ca}\):
For \(^{40}\text{Ca}\), where \(A = 40\), the nuclear density is:
\[
\rho_{\text{Ca}} = \text{constant}.
\]
2. Nuclear Density for \(^{16}\text{O}\):
For \(^{16}\text{O}\), where \(A = 16\), the nuclear density is the same as that of \(^{40}\text{Ca}\):
\[
\rho_{\text{O}} = \text{constant}.
\]
3. Ratio of Densities:
Since the nuclear density is constant for all nuclei:
\[
\frac{\rho_{\text{Ca}}}{\rho_{\text{O}}} = 1.
\]
Final Answer:
\[
\boxed{1}
\]