The heights of two cones are in the ratio 4 : 3 and the radii of their bases are in the ratio 1 : 2. Find the ratio of their volumes.
The heights of two cones are in the ratio 4 : 3 and the radii of their bases are 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
Cone का volume होता है:
$V = \frac{1}{3}\pi r^2 h$
दिया है:
Heights ratio = $4:3$
Radii ratio = $1:2$
अब volume ratio:
$V_1:V_2 = r_1^2h_1 : r_2^2h_2$
$= (1^2 \times 4) : (2^2 \times 3)$
$= 4 : 12$
$= 1 : 3$
Correct Answer: 1 : 3
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