Determine the ratio of the contents of a pot to the (metal) volume of of the pot
You could get rid of many temporary variables, by returning the result right away:

import math
pi = math.pi
class Pot:
    """create a pot with contents, determine the ratio between the contents and the pot"""

    def __init__(self,inner_radius,wall_width,base_thickness,height,content_height):
        self.wall_width = wall_width
        self.inner_radius = inner_radius
        self.outer_radius = self.inner_radius + self.wall_width
        self.base_thickness = base_thickness
        self.height = height
        self.content_height = content_height

    def get_cylinder_volume(self,radius,height):
        return pi * (radius ** 2) * height

    def get_pot_wall(self):
        inner_cylinder = self.get_cylinder_volume(self.inner_radius,self.height)
        outer_cylinder = self.get_cylinder_volume(self.outer_radius,self.height)
        return outer_cylinder - inner_cylinder

    def get_pot_base(self):
        return self.get_cylinder_volume(self.inner_radius,self.base_thickness)

    def get_pot_volume(self):
        return self.get_pot_base() + self.get_pot_wall()

    def get_content(self):
        return self.get_cylinder_volume(self.inner_radius,self.content_height)

    def get_ratio(self):
        return self.get_content()/self.get_pot_volume()

    def check_ratio(self,desired):
        if (self.get_ratio() &lt; desired):
            print ("too small")
        else:
            print (self.get_ratio())


Also, many of your variables are already determined when you initialize the class. Unless you want to change the shape of the pot on the fly (for this I would create a new instance of Pot with the new dimensions), the only thing I would expect to change is the amount of content in the pot. So, pot_wall, pot_base, pot_volume can all be calculated in init and set to variables of the instance:

def __init__(self,inner_radius,wall_width,base_thickness,height,content_height):
        self.inner_radius = inner_radius
        self.content_height = content_height
        outer_radius = inner_radius + wall_width

        self.pot_volume = self.get_cylinder_volume(inner_radius,base_thickness) + self.get_cylinder_volume(outer_radius,height) - self.get_cylinder_volume(inner_radius,height)

...

def get_ratio(self):
    return self.get_content()/self.pot_volume


This would allow you to get rid of get_pot_wall, get_pot_base, get_pot_volume. Or at least the first two, if this is too much inline calculation for you.