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Home » Genis Shock: How This Breakthrough Tech Will Change Your Life Overnight! - Carbonext

Genis Shock: How This Breakthrough Tech Will Change Your Life Overnight! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Express \( h \) in terms of \( r \): \( h = \frac{0.5}{\pi r^2} \).

📌 Lateral area: \( A_{\text{lav}} = 2\pi r h = 2\pi r \cdot \frac{0.5}{\pi r^2} = \frac{1}{r} \)

📌 Top and bottom area: \( A_{\text{topb}} = 2\pi r^2 \)

📌 Total cost:

📌 C(r) = 40 \cdot \frac{1}{r} + 55 \cdot 2\pi r^2 = \frac{40}{r} + 110\pi r^2

📌 To minimize, take derivative:

📌 C'(r) = -\frac{40}{r^2} + 220\pi r

📌 220\pi r = \frac{40}{r^2} \Rightarrow r^3 = \frac{40}{220\pi} = \frac{2}{11\pi}

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