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CylindricalPlot3D[z, {r-range}, {phi-range}, (options...)] plots z as a function of r and phi. CylindricalPlot3D[{z, style},  ...] uses style to render each surface patch.
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Problem 5:
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Part a) Log[z]
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Problem 9:
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Clear["Global`*"];
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Part a) 
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^*)