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

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