Calculating how much whales eat

Was watching a documentary on sea life and they mentioned how much whales eat. I wiki’d it because I forgot the figure (up to 3,600 kilograms (7,900 lb) of krill in a single day - Blue whale - Wikipedia)

My question is: how do they calculate that? Is it just a theoretical estimate based on body size, energy requirements and krill caloric estimates? Or is there some other way that biologists arrive at this figure?

You kill a whale and look at the contents of its digestive system.

I imagine they compare those numbers with some back-of-the-napkin calculations based on the density of krill in the water combined with how much water goes through the whale’s baleen and see if they match up more or less.

I can answer how biologists arrive at some of these estimates, my BiL is a wildlife biologist who studies game birds. (Yes, I know it’s not a whale but it’s an interesting story).

He built a copper prairie chicken and placed an electric heating element inside it. He covered it in the gen-u-ine feathery skin of a real prairie chicken and put it outside. He then ran electricity through the heating element and figured out how many watts it took to keep the chicken at body temperature.

Convert watts to calories and there’s the minimum food intake of a prairie chicken. (He then goes on to figure out how many calories per acre were in the area and calculate the max population of chickens per acre.)

Here’s a quote confirming the other answers so far.

Consumptin of Krill by Minke Whales in Area IV and V of the Atlantic.