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📰 \]Question: A weather balloon is modeled as a sphere with radius $ r $ meters, and it ascends such that its volume increases at a rate proportional to $ \sin \theta $, where $ \theta $ is the angle of elevation from the ground. If the volume increase rate is given by $ \frac{dV}{dt} = k \sin \theta $, and $ \theta = 60^\circ $, compute the rate of volume increase in terms of $ k $ and $ r $. 📰 Solution: The volume of a sphere is given by $ V = \frac{4}{3} \pi r^3 $. Differentiating with respect to time $ t $, we get: 📰 We are given that $ \frac{dV}{dt} = k \sin \theta $, and $ \theta = 60^\circ $, so $ \sin \theta = \frac{\sqrt{3}}{2} $. Substituting: 📰 Pilots See Fire Before Crash Family Of Victims Refuses To Forget 5563164 📰 Hi Cost Of Living 760922 📰 Java Priority Queue Explained The Ultimate Guide To Fast Efficient Task Scheduling 5138131 📰 Knull Venom Last Dance 488476 📰 These New Movies Are Shockingyou Wont Believe Whats Coming This Fall 1266340 📰 Unlock Boom The Ultimate Goudies Lego Set Thatll Free Your Imagination 9643554 📰 Why Gogo Anime Just Became The Hottest Trending Show Of The Year 3775255 📰 Windows 10 Is Not Detecting Second Monitor 6502687 📰 Deceptive Synonym 3864336 📰 Nytimes Exposes Mind Blowing Apple Breakthrough You Need To See Now 8957711 📰 Unlock The Secret To Avoiding Tax Penalties Master Quarterly Payments Instantly 8905645 📰 Travis Scott Fortnite Concert 7659650 📰 You Wont Believe How Everybodys Doing The Wobble Dance Watch The Viral Trend Take Over 8439154 📰 Fight In A School 8669182 📰 How Old Is Claire Danes 8986031