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Home » "Sliding Glass Dance? Install This Cat Door and Watch Them Roam Freely! - 500apps

"Sliding Glass Dance? Install This Cat Door and Watch Them Roam Freely! - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Solution: Let the legs of the right triangle be $ a = 15 $ km and $ b = 20 $ km. The hypotenuse $ c $ is given by the Pythagorean theorem:

📌 c = \sqrt{a^2 + b^2} = \sqrt{15^2 + 20^2} = \sqrt{225 + 400} = \sqrt{625} = 25

📌 The drone travels a distance of $ \boxed{25} $ km.

📌 Question: A hydrologist models a reservoir as a cone with height 60 m and base radius 40 m. A smaller cone (representing a spillway) is similar to the reservoir and has height 15 m. What is the ratio of the volume of the spillway to the reservoir?

📌 Solution: Since the cones are similar, the ratio of their linear dimensions is $ \frac{15}{60} = \frac{1}{4} $. The volume ratio of similar solids is the cube of the linear ratio:

📌 \left(\frac{1}{4}\right)^3 = \frac{1}{64}

📌 The volume ratio is $ \boxed{\frac{1}{64}} $.

📌 Question: A bioinformatician is analyzing a molecular structure shaped like a regular hexagon with side length 6 cm. What is the area of the hexagon?

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