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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 $? 📰 Discover The Powerful Frame Of Wateryour New Secret To Stunning Serene Shots 📰 Discover The Powerful Fruits Of The Spirit Backed By Biblical Scriptures 📰 Discover The Prizes Of Faith Perfect First Communion Gifts Everyone Should Choose 📰 Discover The Revolutionary Flatbutt Technique That Shocked Fitness Pros 📰 Discover The Revolutionary Foster Home For Imaginary Friends Game Changer Inside 📰 Discover The Revolutionary Itinerary Format That Travelers Are Obsessed With 📰 Discover The Secret Behind Stunning Alight Motion Logo Grab This Eye Catching Comic 📰 Discover The Secret Behind The 4 Leaf Clover 4 You Wont Believe How This Symbol Changes Your Luck 📰 Discover The Secret Firework Recipe Thatll Make Your Backyard Blaze 📰 Discover The Secret Flashdancers Club In Nycwhere Style And Rhythm Collide 📰 Discover The Secret Flower Pot Minecraft Trick That Alters Your Game Forever 📰 Discover The Secret Nintendo Ds Game That Broke Players Heartsyou Must See 📰 Discover The Secret Power Of The Four Leaf Clover You Wont Believe What It Does 📰 Discover The Secret Structure That Makes Your Funeral Program Unforgettable 📰 Discover The Secret To Blooming Annual Flowers Every Season