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The sum of volumes of respective parts and the original cone will be same . Hence we have :

1/3 π r^{2} h = 1/3 π (2r/3)^{2} (2h/3) + x

==> x = 1/3 π r^{2} h ( 1 - 8 / 27)

==> x = 1/3 π r^{2} h * (19 / 27)

Hence volume of frustum = 1/3 π r^{2} h * (19 / 27)

Volume of smaller cone = 1/3 π r^{2} h * (8 / 27)

**Hence ratio of volume smaller cone to frustum of cone = 8 : 19**