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Question
If r1 and r2 denote the radii of the circular bases of the frustum of a cone such that r1 > r2, then write the ratio of the height of the cone of which the frustum is a part to the height fo the frustum.
Solution
Since, `Delta VO'B - DeltaVOA `
Therefore,
In `Delta VO'B - DeltaVOA `
`(O'B)/(OA) = (O'V)/(OV)`
`r_2/r_1 = (h -h_1)/(h)`
`r_2/r_2 = 1 - h_1/h`
`h_1/h = 1 - r_2/r_1`
`= (r_1 - r_2)/r_1`
Hence,
The ratio of the height of cone of which the frustum is a part to the height fo the frustum.
\[\frac{OV}{OO'} = \frac{h}{h_1} = \frac{r_1}{r_1 - r_2}\]
Hence, `h : h_1 = r_1 :(r_1 - r_2)`
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