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📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 First, recognize that volume of a cylinder is \( V = \pi r^2 h = 0.5 \) m³.

📌 The total cost includes: lateral surface (\(2\pi r h \times 40\)) and top and bottom (\(2\pi r^2 \times 55\)).

📌 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:

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