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sad meme - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Thus, the ratio is $ \boxed{\frac{\pi}{6}} $.

📌 Question: A pharmacologist is modeling a spherical drug capsule of radius $ r $ and a hemispherical cap of radius $ r $ attached to a cylindrical urodose container of height $ 2r $ and radius $ r $. What is the total volume of the composite object?

📌 Solution: The volume of a hemisphere is $ V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 $.

📌 The volume of the cylinder is $ V_{\text{cyl}} = \pi r^2 h = \pi r^2 (2r) = 2\pi r^3 $.

📌 The total volume is:

📌 V_{\text{total}} = V_{\text{hemisphere}} + V_{\text{cyl}} = \frac{2}{3} \pi r^3 + 2\pi r^3 = \left( \frac{2}{3} + 2 \right) \pi r^3 = \frac{8}{3} \pi r^3

📌 Thus, the total volume is $ \boxed{\frac{8}{3} \pi r^3} $.

📌 Question: A right triangle has legs of lengths $ 5 $ and $ 12 $. What is the length of the shortest altitude?

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