Question : The ratio of curved surface areas of two cones is 1 : 8 and the ratio of their slant heights is 1 : 4. What is the ratio of radii of the two cones?
Option 1: 1 : 1
Option 2: 1 : 2
Option 3: 1 : 4
Option 4: 1 : 8
Correct Answer: 1 : 2
Solution : The curved surface area of a cone $ = \pi rl$ where \(r\) is the radius and \(l\) is the slant height of the cone. Given that the ratio of the curved surface areas of two cones is 1 : 8. $⇒\frac{\pi r_1 l_1}{\pi r_2 l_2} = \frac{1}{8}$ Also, given that the ratio of the slant heights of the two cones is 1 : 4. $⇒\frac{l_1}{l_2} = \frac{1}{4}$ On substituting, $⇒\frac{r_1}{r_2} = \frac{1}{8} \times \frac{4}{1} = \frac{1}{2}$ Hence, the correct answer is 1 : 2.
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Question : 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?
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