The ratio of the curved surface area of two cones is 1 : 4 and the ratio of slant height of the two cones is 2 : 1. What is the ratio of the radius of the two cones?

1 : 8

C.S.A of a cone =\(\pi \)rl

ATQ, ratio of C.S.A of two cones:

⇒ \(\frac{\pi r_1 l_1}{\pi r_2 l_2}\)   = \(\frac{1}{4}\)

⇒ \(\frac{r_1}{r_2}\) × \(\frac{2}{1}\)  = \(\frac{1}{4}\) 

⇒ \(\frac{r_1}{r_2}\) = \(\frac{1}{8}\) 

⇒ r_{1 :} r_{2 = 1 :  8}