A cone and a hemisphere have the same radius, 4.2 cm, and exactly equal volumes. Find the height of the cone.

Set the volumes equal: $\frac{1}{3}\pi r^{2}h=\frac{2}{3}\pi r^3$. Cancelling $\frac{1}{3}\pi r^2$ gives $h=2r=2\times 4.2=8.4$ cm. The answer does not depend on the value of π or even on the radius being 4.2. 4.2 cm assumes $h=r$; 2.8 cm comes from solving as $h=\frac{2r}{3}$; 12.6 cm comes from $h=3r$.