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?
