The volume of a cone is 1408 cm³. If the radius of the cone is 8 cm, then find the height of the cone.

$$\begin{gathered} \mathrm{We} \mathrm{know}, \mathrm{V}=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h} \\ \Rightarrow \mathrm{h}=\frac{3\mathrm{V}}{{\mathrm{\pi r}}^2} \end{gathered}$$

It is given that V = 1408 cm³, r = 8 cm

$\begin{array}{rcl}\mathrm{h} & =& \frac{3\times 1408}{{\displaystyle \frac{22}{7}\times 8^2}}\\ & =& 21 \mathrm{cm}\end{array}$

Thus, the height of the cone is 21 cm.