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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: 📰 Domain Controller Database 📰 Dcouvrez Secret Surveys That Reveal T Houz Of Your Neighbors For Free 5165717 📰 How To Build A Clash Royale Deck That Dominates Every Single Match 5984666 📰 Shotgun King The Final Checkmate 📰 Here Be Dragons 📰 Transform Your Media Experience With The Ultimate Windows 10 Media Tool 7152984 📰 S Corp Examples 801133 📰 3 Alien Earth Timeline Exposes The Shocking Truth About Ancient Alien Visits 3297514 📰 Money Market Accounts Rates 2886936 📰 Public Reaction Wilderness Game And The World Reacts 📰 Pay On Death Bank Of America 📰 Finally Found The Secret To Stop Windows 11 From Hibernatingturn Off Sleep Mode Today 9838396 📰 Dont Miss Thisexperts Reveal The Hidden Power Of Proc You Cant Ignore 8779002 📰 How To Apply For A Business Loan 📰 What Is Erp In Business