By eating a lot of it!
Baleen whales mostly eat krill, which are shrimp-like crustaceans one to two centimetres long |(0.4-0.8inch). This is at the upper end of the size range of organisms considered as plankton, but it’s still tiny compared to a 150 ton blue whale. A blue whale needs about 1.5 million calories daily, which translates to about 40 million krill every single day. Luckily, krill are incredibly numerous. The total mass of the Antarctic krill in the ocean is twice as much as the entire human race. And that’s just one of over 80 species! To catch them, whales lunge forward into thick swarms of krill and take an enormous gulp of krill and seawater. Concertina folds in the skin of the whale’s mouth expand as they gulp up to 90 tons of water at a time. The whale then strains the water out, trapping the krill against a mesh of baleen plates, which are made of keratin, like your fingernails and hair. Depending on the density of the swarm of krill, a blue whale can swallow anything from 8,000 to 450,000 calories in a single mouthful.