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Real-World Applicationshard
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An engineer designs a cylindrical water tank with a hemispherical top. The cylindrical portion has radius rrr meters and height hhh meters. The total volume is constrained to be 100 cubic meters. The surface area (lateral side of cylinder + hemispherical top, excluding the bottom) must be minimized. If the optimal radius is approximately r0r_0r0​ meters, which expression represents the optimal height h0h_0h0​ in terms of r0r_0r0​?