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.

Answer 1

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)`