The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former.

Question:

The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former. The ratio of their radii is
(a) 2 : 1
(b) 4 : 1
(c) 8 : 1
(d) 1 : 1

 

Solution:

(b) 4 : 1
If the slant height of the first cone is l, then the slant height of the second cone will be 2l.
Let the radii of the first and second cones be r and R, respectively.
Then we have:

$\pi r l=2 \times(\pi R \times 2 l)$

$\Rightarrow r=4 R$

$\Rightarrow \frac{r}{R}=\frac{4}{1}$

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