Question 126

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?

Solution

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 = 1 : 27

=> Ans - (C)

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