There are two cones. The curved surface area of one is twice that of the other. The slant height of the later is twice that of the former. Find the ratio of their radii.

 Given:

The curved surface area of one cone is twice that of the other.

The slant height of the latter is twice that of the former.

To do:

We have to find the ratio of their radii.

Solution:

Let $r_1$ and $r_2$ be the radii of the two cones.

Let the height of the first cone be $h$ and the height of the second cone be $2h$.

Therefore,

Curved surface of the first cone $= 2 \pi r_1h$

Curved surface area of the second cone $=2 \pi r_{2} \times 2 h$

$=4 \pi r_{2} h$

This implies,

$2 \pi r_{1} h=2 \times 4 \pi r_{2} h$

$2 \pi r_{1} h=8 \pi r_{2} h$

$r_{1}=4 r_{2}$

$\frac{r_{1}}{r_{2}}=\frac{4}{1}$

Ratio of their radii is $4: 1$.

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Updated on: 10-Oct-2022

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