Derive the formula for the volume of the frustum of a cone.

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 △ABG and △ADF, DF || BG
Therefore, △ABG ≅ △ADF
DF/BG = AF/AG = AD/AB
=> r2/r1 = h1-h/h1 = l1-l/l1
=> r2/r1 = 1 - h/h1 = 1 - l/l1
=> 1 - h/h1 = r2/r1
=> h/h1 = 1 - r2/r1 = r1 - r2/r1
=> h1/h = r1/r1 - r2
=> h1 = r1h/r1 - r2
Volume of frustum of cone = Volume of cone ABC - Volume of cone ADE
= (1/3)πr1²h1 - (1/3)πr2²(h1 - h)
= π/3[r1²h1 - r2²(h1 - h)]
= π/3[r1²(r1h/r1 - r2) - r2²(r1h/r1 - r2 - h)]
= π/3[(r1³h/r1 - r2) - r2²(h(r1 - r2)/r1 - r2)]
= π/3[(r1³h/r1 - r2) - r2²h(r1 - r2)/r1 - r2]
= π/3h[r1³ - r2³/r1 - r2]
= π/3h[(r1 - r2)(r1² + r2² + r1r2)/r1 - r2]
= (1/3)πh[r1² + r2² + r1r2]