55^2 \equiv 0^2 = 0 \pmod{11}

February 22, 2026

$55^2 \equiv 0^2 = 0 \pmod{11}$

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Now compute \( 3025 \mod 11 \).
First, reduce 55 modulo 11:
\div 11 = 5 \quad \Rightarrow \quad 55 \equiv 0 \pmod{11}
\equiv 0 \pmod{11}
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?

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