Finding the charge density that produces a specific field

[Neolightdraco]

Homework Statement

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Using Gauss law,

Since there has been no mention of which type of charge density we have to find out I assumed it to be surface charge density since Gauss Law is in surface intergration , and I don't think there is any need to doing integration since the options given are results obtained without integration , I just can't get what's wrong

Is the problem in my choice of charge density or my method of solving it wrong?

Homework Equations

The Attempt at a Solution

 

[kuruman]

Have you tried Gauss's Law in differential form?

 

[Neolightdraco]

Have you tried Gauss's Law in differential form?

No, I will try that