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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: 📰 Hhs Autism Shocked Mewhy This Condition Gets More Attention Than Ever 624368 📰 Hilton Garden Inn Times Square 9026311 📰 Average Salary Of American 8926679 📰 How To Set Outlook Rules Like A Pro Boost Productivity Instantly 8098397 📰 A Geometric Sequence Has First Term 3 And Common Ratio 2 Find The Sum Of The First 8 Terms Then Find The 8Th Term 227831 📰 5 Is Flynn Breaking Bad Now Unleashing Secrets No One Expected Find Out 2192009 📰 Miax Stock Could This Underdog Trigger The Next Big Financial Revolution 2341433 📰 Ghosted By A Friend 6143872 📰 Top Stocks Guaranteed To Skyrocket Todayinvest Before Its Too Late 3489617 📰 You Wont Believe What Happens When You Try Vr With A Headsetshocking Results 239907 📰 Jp France 1681693 📰 F0 0 9129999 📰 The Visitor Games Revealed The Shocking Twist Thatll Change Everything 3863423 📰 What Boston Prayers Have Claimed Miracle Moments In The City 2392966 📰 Pof Login Pof 6901825