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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: 📰 Step Into The Past Retro Golf Game Lets You Swing Like Legendsplay On Chrome Today 5702209 📰 Roblox Roller Skates 6718136 📰 Race To The Witch 466704 📰 But Instruction Generate Math Problem So Keep Precise 5193051 📰 The Secret Ingredient Making Pecorino Romano Unforgettable 7870573 📰 Gpu News Youre Ignoringcould Change Gaming Forever 6119782 📰 Compare Travel Cards 1192409 📰 Salmon Seasoning 708095 📰 How To Revamp Classic Outlook Themes Secrets Revealed To Look Sharp Instantly 8806514 📰 Fullscripts 4902857 📰 Free Kick Chaos The Ultimate Game That Drops Your Opponents Like Crazy 9596908 📰 The Untold Truth About Alva Jayyoull Run For The Keyboard 8513394 📰 New York Pizzeria 3348365 📰 You Wont Believe What 100 In Silver Can Earn Youstart Investing Now 2622611 📰 Banks To Open Account 1466625