The curved surface area of one cone is twice that of other cone while the slant height of second cone is twice that of first cone. Find the ratio of their radii.

2:1

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4:1

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8:1

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1:1

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Solution

The correct option is B 2:1
Curved surface area of A is given by $A = π r l$ where r is the radius of the cone and l is slant height.
The curved surface area of one cone is twice that other.
i.e., $A_{1} = 2 A_{2}$
$π r_{1} l_{1} = 2 π r_{2} l_{2}$
$r_{1} l_{1} = 2 r_{2} l_{2}$ .....(1)
Again the slant height of second is twice of first
$l_{2} = 2 l_{1}$ .......(2)
Thus, from 1,
$r_{1} l_{1} = 2 r_{2} (2 l_{1})$
$r_{1} = 4 r_{2}$
$r_{1} : r_{2} = 4 : 1$
Thus, option B is correct.

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