The ratio of curved surface area of two cones is 1 : 9 and the ratio of slant height of the two cones is 3 : 1. What is the ratio of the radius of the two cones?
Let radius of the cones be $$r_1$$ cm and $$r_2$$ cm respectively.
Slant height of first cone = $$l_1=3$$ cm and of second cone = $$l_2=1$$ cm
Curved surface area of cone = $$\pi rl$$
According to ques, => $$\frac{\pi r_1l_1}{\pi r_2l_2}=\frac{1}{9}$$
=> $$\frac{r_1}{r_2}=\frac{1}{9}\times\frac{1}{3}=\frac{1}{27}$$
Thus, the ratio of the radius of the two cones =Â 1Â : 27
=> Ans - (C)
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