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📰 Question: A carbon nanotube is modeled as a cylinder with radius $ r $ and height $ h $. If its lateral surface area equals the area of a circle with radius $ 2r $, what is the ratio $ \frac{h}{r} $? 📰 Solution: The lateral surface area of a cylinder is $ 2\pi r h $. The area of a circle with radius $ 2r $ is $ \pi (2r)^2 = 4\pi r^2 $. Setting them equal: $ 2\pi r h = 4\pi r^2 $. Cancel $ 2\pi r $ to get $ h = 2r $. Thus, the ratio $ \frac{h}{r} = \boxed{2} $. 📰 Question: A circle is inscribed in a square with side length $ s $. What is the ratio of the circle’s area to the square’s area, expressed in terms of $ \pi $? 📰 Carolina Kitchen Menu 7646130 📰 Pikpak The Secret Feature Trend Shaking The Mobile App World Right Now 914683 📰 A X L Rose 2404148 📰 Purple Corn The Superfood Thats Taking Over The World Heres Why You Need It Now 1541734 📰 Best Idle Games On Steam 6402881 📰 Jd Vance Edits 9985695 📰 Vintage Park Apartments 5187002 📰 1Usd To Eur 5199427 📰 5 Oclock Shadow 6332372 📰 Truck Games Free Race Crash And Wininstall Now Game Like Champions 1144422 📰 This Simple Command Unlocks Elite Powershell Scripting Capabilities 5394251 📰 Youll Never Guess How Dexter Mom Transformed Her Homeschool Into A Social Media Sensation 3888455 📰 Logo Maker Free Online 766253 📰 Eyes Open Legendary Coffee Fueled Manga Magic Awaits 4441622 📰 You Wont Believe How Han Solo Almost Didnt Survive The Death Star Trap 3006298