A cone is divided into 3 parts with equal height find the volume of each cone and frustum - Maths - Surface Areas and Volumes

Question

A cone is divided into 3 parts with equal height find the volume of
each cone and frustum ?

Anuradha Sharma · Accepted Answer

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Let the radius of original cone AHD is r so We know that triangle AFC and AED are similar so AFAE=FCED2h3h=FCr⇒FC=2r3Similarly GB=r3So volume of cone AHED=13πr2×3h
=πr2hNow for cone AFC, volume = 13π×FC2×2h=13π×4r29×2h=827πr2hNow volume of cone AGB, =13π×GB2×h=13π×r29×h=127πr2hNow Volume of frustum GBFC=Volume of cone AFC-volume of cone AGB=827πr2h-127πr2h=727πr2hAnd volume of frustum BCDEH=Volume of AHD-volume of AGB=πr2h-127πr2h=2627πr2h

A cone is divided into 3 parts with equal height find the volume of each cone and frustum ?