So, ".35 qt" seemed a bit of an odd size to me. I did the math and it works out to 11.2 oz. That is just under 1 1/2 cups. Or, to use my favorite unit of measure, just under the capacity of bottle of beer.
Another point of reference might be the Thermos funtainers my kids used to use in their lunchboxes for elementary school (https://www.amazon.com/Thermos-Funtainer-Ounce-Food-Batman/dp/B004CEJYCA). These hold 10 oz, so I guess the capacities are pretty close.