Q. 74.3( 72 Votes )

Derive the formula for the volume of the frustum of a cone, given to you in Section 13.5,using the symbols as explained

Answer :

Let ABC be a cone.

And,


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


Now,


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 – =


=


h1 =


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


= r12h1 - πr22 (h1 – h)


= [r12h1 – r22 (h1 – h)]


= [r12 () – r22 ( - h)]


= [ - ]


= * h [ ]


= h []


= h [ r12 + r22 + r1r2]


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