The height of right circular cone is trisected by two plane parallel to its base. Show that the volume of the three propotion from top are in ratio 1:7:19.
Let VAB be a right circular cone of height 3h and base radius r. Thus cone is cut by planes parallel to base at point of and L such that VL = L O´ = h.
Since ∆VOA and ∆VB´A´ are similar
Also ∆VOA ~ ∆VLC
Let V1 be the volume of cone VCD then
Let V2 be the volume of the frustum A´B´DC. Then
Let V3 be the volume of the frustum ABB´A´. Then