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Home » Let the integers be \(x\), \(x+1\), and \(x+2\). - Abbey Badges

Let the integers be \(x\), \(x+1\), and \(x+2\). - Abbey Badges

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 Therefore, the remainder is:

📌 \]Liam is designing a cylindrical water tank that must hold exactly 500 liters (equivalent to 0.5 m³) of water. If the material cost for the curved lateral surface is $40 per m² and the top and bottom each cost $55 per m² due to thicker reinforcement, what is the minimum cost to construct the tank, minimizing the surface area?

📌 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:

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