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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: 📰 Frontier Availability 📰 Poufs That Double As Furniture Heres The Must Have Trend You Need Now 814848 📰 The Ultimate Beneficiary Ira Rmd Calculator Drastically Reduce Your Tax Bill 7651440 📰 Hero Of Cinder City Genshin 📰 Pharmacy Advantage Secrets To Smarter Prescriptions Massive Savings 6744519 📰 What Time Is Breakfast Over In Mcdonalds 1542309 📰 H15 5152 15015 100 5225 2250 100 1125 2250 100 1225 Meters 8538202 📰 Mutilate Doll 📰 Credit Card For My Business 📰 Walmart Beta 📰 You Wont Believe How Fast Microsoft Edge Surf Bots Like A Proturbo Tech Revealed 4460814 📰 When Can You Play Fortnite 📰 Regarded As A Hidden Gemhow Cwh Stock Price Could Boost Your Portfolio Today 6385486 📰 Best Buy Credit Card Login Citi 4083882 📰 Data Shows North Carolina Age Consent And The Situation Escalates