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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: 📰 X Men Legends 2 Rise Of Apocalypse Cheats 8890479 📰 Bhel Share Rate Surpasses Expectationsheres What You Need To Know Now 3999592 📰 Grow A Girlfriend 2495152 📰 Perejil 4896664 📰 Best Free Movie Streaming Sites 6626271 📰 Call Center Solutions 3078051 📰 White Cowboy Boots The Secret Trend Thats Taking The World By Storm Glam Or Blunder 9983337 📰 Vigilante Kdrama 8932616 📰 Green Dunks That Make Pros Split Their Eyesis This Shoe The Future 3418093 📰 Biliard 8 Ball 2608297 📰 You Wont Believe Whats Inside Cooperstown Hall Of Fame These Hidden Treasures Will Shock You 1911880 📰 Revolutionize Your Business Unlock Hidden Dynamics In Business Central 7416973 📰 Dotnet User Secrets 9654098 📰 The Forgotten Mana Collection Thats Taking The Gaming World By Storm Discover It Now 8460823 📰 Job Training Programs 4491338