Real-World Applicationshard
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An engineer designs a cylindrical water tank with a hemispherical top. The cylindrical portion has radius rr meters and height hh 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_0 meters, which expression represents the optimal height h0h_0 in terms of r0r_0?