Cone height $h_{c}$ = 19 cm. Cylinder radius $r_{y}$ = (1/3) * Cone radius $r_{c}$. The cone is filled with water.

Since $V_{cone} = V_{cyl}$, equate $\frac{1}{3} \pi r_c^2 (19) = \pi (\frac{r_c}{3})^2 h_y$. The $\pi$ and $r_c^2$ terms cancel, leaving $h_y = 19 \times 3 = 57$ cm.

Students often forget to square the ratio $1/3$ when substituting the radius, leading to $h_y = 19 \times 3 = 57$ rather than $19 \times 3^2 = 171$.

This concept is a precursor to fluid dynamics and surface area problems often appearing in mechanical engineering aptitude sections.