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
4:1
Let r be the radius and l be the slant height
∴ Curved surface area of first cone=πr1l1
and curved surface area of second cone=πr2l2
But l2=2l1and
πr1l1=2πr2l2∴πr1l1πr2l2=21r1l1r2l2=21But l2=2l1∴r1l1r22l1=21⇒r12r2=21⇒r1r2=41∴ Ratio of radii=4:1