(c) πh2 sec α tan α
S = πrl, where r = radius, l = slant height, h = height
Now \(\frac{r}{h}\) = tan α ⇒ r = h tan α
l = \(\sqrt{h^2+r^2}\)
= \(\sqrt{h^2+r^2\,tan^2\,α}\)
= \(\sqrt{h^2(1+tan^2\,α)}\)
= \(\sqrt{h^2\,sec^2\,α}\) = h sec α
∴ S = π. h tan α. h sec α = πh2 sec α tan α.