Answer :

Let ABC be a cone.

And,

A frustum DECB is cut by a plane parallel to its base

Now,

Let *r*1 and *r*2 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 – =

=

*h*1 =

Volume of frustum of cone = Volume of cone ABC - Volume of cone ADE

= r1^{2}h1 - πr2^{2} (h1 – h)

= [r1^{2}h1 – r2^{2} (h1 – h)]

= [r1^{2} () – r2^{2} ( - h)]

= [ - ]

= * h [ ]

= h []

= h [ r1^{2} + r2^{2} + r1r2]

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