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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}} 📰 Top 3 Person Picks That Every Gamer Should Download Now 5439040 📰 Free Bloons Tower Defense This Simple Game Will Take Over Your Weekend 8118953 📰 How A Tiny Spot Difference Noticed Can Transform Your Entire Daily Experience 4670268 📰 Why This Vizio Tv Remote Heats Up The Point Youre Not Seeing 5160958 📰 The Ultimate Guide To Net Benefits Fidelity Boost Your Returns Like Never Before 4897058 📰 From Ichiro To Sakamoto The Untold Secrets Behind These Iconic Characters You Love 2943554 📰 The Revolutionary Gerson Therapy Pdf Secret That No Doctor Ever Told You 9531283 📰 Fighting Weakness 7170356 📰 5 Inside Oracle Federal Forum Hidden Agendas And Game Changing Insights Exposed 6202505 📰 The Ultimate Guide To Faster Hair Growth See Results In 7 Days Naturally 2826112 📰 Gallery Google Photos 1855090 📰 Wells Fargo Arden Way 6528227 📰 Pocket Mirror 3758773 📰 Gangland Alive Shocking Clips That Will Make Your Skin Crawl 5097637 📰 Copart Stock 975372