The coelenteron, also known as the gastrovascular cavity, is a characteristic feature of the phylum Cnidaria, which includes organisms like Hydra. It is a central cavity that serves multiple functions within the body of Hydra. The double purpose of the coelenteron includes digestion and circulation.

Digestion:
The coelenteron acts as a site for both extracellular and intracellular digestion in Hydra. Extracellular digestion occurs when Hydra captures its prey, typically small invertebrates, using its tentacles equipped with specialized cells called cnidocytes. These cnidocytes contain stinging cells called nematocysts, which inject venom into the prey and immobilize it. The prey is then engulfed by the Hydra and enters the coelenteron.

Once inside the coelenteron, the prey is exposed to digestive enzymes secreted by the gland cells lining the cavity. These enzymes break down the prey's proteins, carbohydrates, and fats into simpler molecules that can be absorbed by the cells. The partially digested food is then taken up by the endodermal cells lining the coelenteron through phagocytosis, a process in which the cell engulfs and absorbs the food particles.

Intracellular digestion takes place within the endodermal cells themselves. The engulfed food particles are enclosed in food vacuoles within the cells. These food vacuoles fuse with lysosomes, which contain digestive enzymes. The enzymes in the lysosomes further break down the food particles into smaller molecules, which are then absorbed by the endodermal cells and utilized for energy and growth.

Circulation:
The coelenteron of Hydra also serves as a circulatory system, although it is not as efficient as the closed circulatory systems found in higher organisms. The fluid-filled coelenteron allows for the distribution of nutrients, oxygen, and waste products throughout the body of Hydra.

As digestion takes place in the coelenteron, nutrients from the digested food are absorbed by the endodermal cells and released into the coelenteron fluid. This nutrient-rich fluid circulates throughout the body, supplying nutrients to all the cells.

Similarly, waste products generated during metabolism are also released into the coelenteron fluid. The waste products, such as carbon dioxide and ammonia, are then eliminated through the mouth or through simple diffusion across the body wall.

Overall, the coelenteron of Hydra serves the double purpose of digestion and circulation. It provides a central cavity for the digestion of prey and the absorption of nutrients, while also facilitating the distribution of nutrients and elimination of waste products throughout the body.

Option A is absolutely correct.