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Derive the formula for the curved surface area and total surface area of the frustum of cone.

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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

∴ ΔABG ∼ ΔADF 

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

CSA of frustum = π(r1+r2)l

Total surface area of frustum 

=CSA of frustum + Area of upper circular end + Area of lower circular end

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