Mensuration Prob #4

[papgust]

If the curved surface area of a cone is thrice that of another cone and slant height of the second cone is thrice that of the first cone, find the ratio of the area of their base.

OA is [spoiler]81:1[/spoiler]. somehow i'm not getting this answer. Can someone explain me?

[xcusemeplz2009]

curved SA of a cone=pi*r*L

let r1 and l1 for 1st cone
and r2 and l2 for 2nd

Csa of 1st=3( Csa of2nd)
pi*r1*l1=3pi*r2*l2=>r1l1=3r2l2

l2=3l1

therefore r1*l1=9r2*l2
i.e r1=9r2

base=pi r^2
ratio is pi r1^2/pi r2^2=> 81:1