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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: 📰 Surprise How Fast You Can Drive With This Hidden Nu Car Rental Deal 2291178 📰 Install Vlc Player Mac 2080244 📰 Top 10 Proven Tricks To Become A Viral Meme Designer Overnight 3622030 📰 Design Like A Pro How The Microsoft Fabric Icon Revolutionizes Workplace Innovation 4025847 📰 Can You Solve The Sorting Game Masterpiece Unlock Hidden Skills Today 6752565 📰 Why Every Successful Investor Knows Passive Income Means And How To Get It 1025304 📰 Discover The Free War Games That Are Taking The Military Gamers By Storm 4552120 📰 Bild From Confusion To Profit Master Your Cma Account In Minutes 7037420 📰 Nohc Stock The Fastest Growing Investment You Cant Afford To Miss 7764681 📰 Perplexity Logo 3140688 📰 Game Robot Game Robot Do Gamers Need Robots Watch This Insane Automated Gameplay Breakthrough 7046980 📰 Finally Revealed The Ultimate Guide To Mastering Medias Average Arithmetic Numbers 6790639 📰 Gmail Forgot Password 2318498 📰 What Are The Best Toothpastes For Whitening 2308569 📰 Alicia Dove 1492594