Verified by Ajay Kumar
A hemispherical tank has an inner radius of 3 m. It is filled with water at a rate of 1800π liters per minute. How long will it take to fill the tank completely? (Note: 1 m^3 = 1000 liters)
12 minutes
10 minutes
5 minutes
15 minutes
Answer: B
Volume of a hemisphere = \(\frac{2}{3}\pi r^3\). For \(r=3\), volume = \(\frac{2}{3}\pi\times3^3=18\pi\) m^3. In litres, volume = \(18\pi\times1000=18000\pi\) litres. Time = \(\frac{18000\pi}{1800\pi}=10\) minutes. Trick: Divide the total volume by the filling rate.
एक अर्धगोलाकार टैंक की आंतरिक त्रिज्या 3 मीटर है। इसे 1800π लीटर प्रति मिनट की दर से पानी से भरा जाता है। टैंक को पूरी तरह भरने में कितना समय लगेगा? (ध्यान दें: 1 m^3 = 1000 लीटर)
12 मिनट
10 मिनट
5 मिनट
15 मिनट
उत्तर: B
अर्धगोले का आयतन = \(\frac{2}{3}\pi r^3\)। \(r=3\) रखने पर आयतन = \(\frac{2}{3}\pi\times3^3=18\pi\) m^3। लीटर में आयतन = \(18\pi\times1000=18000\pi\) लीटर। समय = \(\frac{18000\pi}{1800\pi}=10\) मिनट। ट्रिक: कुल आयतन को भरने की दर से भाग दें।
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