Question
Download Solution PDFTwo 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Heights ratio (h1 : h2) = 4 : 3
Radii ratio (r1 : r2) = 1 : 2
Formula used:
Volume of cone (V) = (1/3)πr2h
Calculation:
Let heights be h1 = 4k and h2 = 3k
Let radii be r1 = k and r2 = 2k
V1 = (1/3)π(k)2(4k)
⇒ V1 = (1/3)πk3 × 4
V2 = (1/3)π(2k)2(3k)
⇒ V2 = (1/3)π4k2 × 3k
⇒ V2 = (1/3)π4k3 × 3
Ratio of volumes = V1 : V2
⇒ (1/3)πk3 × 4 : (1/3)π4k3 × 3
⇒ 4k3 : 12k3
⇒ 1 : 3
∴ The correct answer is option 1.
Last updated on Jul 8, 2025
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