The sum of volumes of respective parts and the original cone will be same . Hence we have :
1/3 π r2 h = 1/3 π (2r/3)2 (2h/3) + x
==> x = 1/3 π r2 h ( 1 - 8 / 27)
==> x = 1/3 π r2 h * (19 / 27)
Hence volume of frustum = 1/3 π r2 h * (19 / 27)
Volume of smaller cone = 1/3 π r2 h * (8 / 27)
Hence ratio of volume smaller cone to frustum of cone = 8 : 19