A conical hollow is scooped out of a solid cylinder of radius 6 cm and height 8 cm: the cone has the same radius, its open mouth is the whole top face of the cylinder and its point reaches the centre of the bottom face. Find the total surface area of the solid left, in ${\text{cm}}^2$, in terms of π.

The cone's slant height = √$(6^2+8^2)=$ √100 = 10 cm. Three surfaces survive: the bottom circle π$r^2=36$π, the outer curved surface 2πrh = 96π, and the sloping wall of the hollow, which is the cone's curved surface πrl = 60π. Total = 36π + 96π + 60π = 192π ${\text{cm}}^2$. (Forgetting the bottom circle gives 156π; the mouth swallows the whole top face, so counting a top circle as well, 228π, is wrong; using the cone's flat base 36π instead of its curved wall 60π gives 132π.)