Let ABC be a cone. A frustum DECB is cut by a plane parallel to its base. Let r1 and r2 be the radii of the ends of the frustum of the cone and h be the height of the frustum of the cone

In ΔABG and ΔADF, DF||BG

= =

= =

= 1 - = 1 -

1 - =

= 1 – =

=

l1 =

CSA of frustum DECB = CSA of cone ABC - CSA cone ADE

= πr1l1 – πr2 (l1 - l)

= πr1 () – πr2 []

= –

= πl [ ]

CSA = π (r1 + r2) * l

Total surface area of frustum = CSA + Area of upper circular end + Area of lower circular end

= π (r1 + r2) * l + πr2² + πr1²

= π [(r1 + r2) * l + r1² + r2²]