A solid cone of base radius 9 cm and vertical height 12 cm is sliced right through by a plane containing its axis. Find the area of the flat triangular face exposed on one of the pieces, in ${\text{cm}}^2$.

A cut along the axis exposes a triangle whose base is the full diameter, 18 cm, and whose height is the cone's vertical height, 12 cm. Area = ½ × $18\times 12=108{\text{cm}}^2$. (Using the radius 9 cm as the base gives $54{\text{cm}}^2$; using the slant height 15 cm in place of the vertical height gives $135{\text{cm}}^2$; $216{\text{cm}}^2$ drops the ½.)