The radius and the height of right circular cone are in the ratio 5 : 12. If its volume is 314 metre³, the diameter of its base is equal to (π = 3.14) :एक समवृत्तीय शंकु की त्रिज्या और ऊँचाई में 5 : 12 का अनुपात है। यदि इसका आयतन 314 मीटर³ है, तो इसके आधार का व्यास बराबर है (π = 3.14) :

1. A10 metres10 मीटर
2. B5 metres5 मीटर
3. C20 metres20 मीटर
4. D15 metres15 मीटर

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: A. 10 metres10 मीटर

Explanation

Let r = 5k and h = 12k. Volume = (1/3)πr²h = (1/3) × 3.14 × 25k² × 12k = 314k³. Setting 314k³ = 314 gives k = 1, so r = 5 m and the diameter = 10 metres.माना r = 5k तथा h = 12k। आयतन = (1/3)πr²h = (1/3) × 3.14 × 25k² × 12k = 314k³। 314k³ = 314 रखने पर k = 1, अतः r = 5 मीटर तथा व्यास = 10 मीटर।