The height and radius of the cone of which the frustum is a part are `h_1` and `r_1` respectively. If `h_2` and `r_2` are the heights and radius of the smaller base of the frustum respectively and `h_2\ : h_1=1\ :2` , then `r_2\ : r_1` is equal to (a) `1\ :3` (b) `1\ :2` (c) `2\ :1` (d) `3\ :1`

Explanation

`triangle A O V and L O iota V` are similar triangles,


i In `triangle A O V and L O I V`



`frac{O A}{O^{prime} L}=frac{O V}{O^{prime} V} `


`Rightarrow frac{r_{1}}{r_{2}}=frac{h_{1}}{h_{1}-h_{2}} `


`Rightarrow(h_{1}-h_{2}) r_{1}=h_{1} r_{2} `


`Rightarrow r_{1} h_{1}-r_{1} h_{2}=h_{1} r_{2} `


`Rightarrow r_{1} h_{1}-h_{1} r_{2}=r_{1} h_{2} `


...