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A right circular cone of height h’ is cut by a plane parallel to the base and at a distance h/3 from the vertex, then the volumes of the resulting cone and frustum are in the ratio:

- 1 : 3
- 8 : 19
- 1 : 4
- 1 : 7

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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**

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