Two cones have their heights in the ratio 4 : 3
Two cones have their heights in the ratio 4 : 3 and the radii of their bases in the ratio 1 : 2. Find the ratio of their volumes.
दो शंकुओं की ऊँचाइयाँ का अनुपात 4 : 3 हैं तथा उनके आधारों के त्रिज्याओं का अनुपात 1 : 2 में हैं। उनके आयतनों का अनुपात ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
1 : 3
h1 : h2 = 4 : 3, r1 : r2 = 1 : 2
Volume of a cone: V = $ \frac{1}{3} \pi r^2 $ h
V1 : V2 = $\frac{1}{3} \pi r1^2 h1 : \frac{1}{3} \pi r2^2$ h2
V1 : V2 = $ r1^2 h1 : r2^2 h2 $
Substitute the given ratios:
V1 : V2 = $ 1^2 \cdot 4 : 2^2 \cdot 3 $
V1 : V2 = 4 : 12
V1 : V2 = 1 : 3
Answer = 1 : 3
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