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Home » These Mad Scientists Are Pushing Limits—Watch Their Wildest, Most Dangerous Experiments! - Dyverse

These Mad Scientists Are Pushing Limits—Watch Their Wildest, Most Dangerous Experiments! - Dyverse

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 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?

📌 Solution: The area of the triangle is:

📌 A = \frac{1}{2} \cdot 5 \cdot 12 = 30

📌 The hypotenuse is:

📌 c = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13

📌 Altitude to leg 5: $ h_5 = \frac{2A}{5} = \frac{60}{5} = 12 $

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