Question

A right circular cone is divided into three parts trisecting its height by two planes drawn parallel to the base. Show that volumes of the three portions starting from the top are in the ratio 1:7:19

Answer 1

Let the radii of three cones from top be r1,r2 and r3 respectively.

Let the height of given cone be 3 h.

so, the height of cone ADE = 2 h and height of cone ABC =h

Volume of frustum DEGF

Hence, required ratio = 1 : 7 : 19.