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📰 Solution: The area of an equilateral triangle is given by $ \frac{\sqrt{3}}{4} s^2 $, where $ s $ is the side length. Setting $ \frac{\sqrt{3}}{4} s^2 = 36\sqrt{3} $, we solve for $ s^2 = 144 $, so $ s = 12 \, \text{cm} $. The new side length is $ 12 - 4 = 8 \, \text{cm} $. The new area is $ \frac{\sqrt{3}}{4} \times 8^2 = 16\sqrt{3} \, \text{cm}^2 $. The decrease in area is $ 36\sqrt{3} - 16\sqrt{3} = 20\sqrt{3} \, \text{cm}^2 $. \boxed{20\sqrt{3}} 📰 Question: A spherical data storage unit has a radius of $ y $ units, and a hemispherical backup dome has a radius of $ 3y $ units. What is the ratio of the storage unit's volume to the backup dome's volume? 📰 Solution: The volume of a sphere is $ \frac{4}{3}\pi y^3 $, and the volume of a hemisphere is $ \frac{2}{3}\pi (3y)^3 = \frac{2}{3}\pi \times 27y^3 = 18\pi y^3 $. The ratio is $ \frac{\frac{4}{3}\pi y^3}{18\pi y^3} = \frac{4}{54} = \frac{2}{27} $. \boxed{\dfrac{2}{27}} 📰 Dow Inc Stock Breakthrough Why Investors Are Selling Out Tonight 9874659 📰 Rurouni Kenshin Movie Reveals The Hidden Truth No Fan Knewyour Heart Will Skip A Beat 7858421 📰 Buffalo Wild Wings Weekly Specials 3584306 📰 Unlock Your Inner Artist Easy Cartoon Characters To Draw That Everyone Will Love 66599 📰 Lost Your Windows Key This Method Gets It Back In Seconds 9438829 📰 The Ultimate X Men Cast Lineup You Wont Believe Is Coming 7750469 📰 First Day Of Summer 2024 6844142 📰 Morawiec Ist Ein Ruhiges Dorf In Der Gmina Smolenttbtessaue Historischer Landwirtschaftlicher Kern Mit Bewahrtem Flair Ideal Fr Alle Die Ruhige Lndliche Umgebung Mit Kultureller Tiefe Suchen 6927679 📰 Maximum 401K Secrets Boost Savings Faster Than Everdont Miss This 4836169 📰 2 Player Game Thatll Have You Screaming In Joy Guess Who Recreated This 7004878 📰 Bank Foreclosures 2085334 📰 What Are The Real Names Of Snow Whites Seven Dwarfs Heres The Surprising Truth 8724489 📰 Wells Fargo Credit Card 0 Apr 21 Months 7796537 📰 Subito Miracle Unlock Fast Deliveries In Secondsstart Using It Today 8937051 📰 Zetamac Hacks Unlock Minds Slash Lag And Dominating The Gaming Scene 127825