The radii of two cones are in the ratio 2:1 and their volumes are equal. The ratio of their heights is:

Question

The radii of two cones are in the ratio 2:1 and their volumes are equal. The ratio of their heights is:

1. A. 1:2
2. B. 2:1
3. C. 1:4 (Correct answer)
4. D. 1:8

Correct Answer

Option C — 1:4

Detailed Solution & Explanation

The correct answer is 1:4.

Key Points

• Volume of cone = (1/3)πr²h.
• Equal volumes: r₁²h₁ = r₂²h₂.
• With r₁:r₂ = 2:1 → 4h₁ = h₂ → h₁:h₂ = 1:4.

प्रश्न (हिन्दी में)

दो शंकुओं की त्रिज्याएँ 2:1 के अनुपात में हैं और उनके आयतन बराबर हैं। उनकी ऊँचाइयों का अनुपात है:

1. A. 1:2
2. B. 2:1
3. C. 1:4
4. D. 1:8