The height of a right circular cone is trisected by two planes drawn parallel to the base. Show that the volumes of the three portions starting from the top are in the ratio 1:7:19.

Explanation

Let V AB be a right circular cone of height 3h and base radius r.

This cone is cut by planes parallel to its base at point O’ and L such that` V L = LO’ = h`

Since triangles V OA and O’A’ are similar

`:. V’O/VO = O’A’/OA`

`r/r1 = 3h/2h`

`r1 = 2r/3`

also` /_\VOA ~ /_\VLC`

:.` VO/VL = OA/LC`

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