Explanation:

- Corpulent means having a large, bulky body, often used synonymously with being overweight or fat.

- Option 1: Lean implies being slim and lacking excess body fat. It is quite the opposite of corpulent.

- Option 2: Gaunt suggests being thin and bony, typically because of suffering, hunger, or age. It is not a synonym for corpulent.

- Option 3: Emaciated means being extremely thin or weak, typically due to severe lack of nutrition, which is opposite to being corpulent.

- Option 4: Obese refers to having excessive body weight or fat, which is synonymous with corpulent.

- Obese is the correct synonym for corpulent, as both imply an excessively large amount of body fat.