Where does a barrel cactus store water?

A barrel cactus [Echinocactus and Ferocactusspp] stores water in its stem. A cactus plant is all about energy, water and work conservation. So water, nutrient solutions, and energizing photosynthetic products all are stored where they're most needed, in the stem. It's a question of specialization of body parts and body functions. Otherwise, energy, time and work are spent and wasted shuttling water and watery products and solutions back and forth between the above ground shoots and the below ground roots.