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}