Final answer:
To visualize a pneumoperitoneum in a patient unable to stand, the left lateral decubitus and dorsal decubitus positions with appropriate projections are used, enabling the detection of free air in the abdominal cavity.
Step-by-step explanation:
To demonstrate a pneumoperitoneum on a patient who is too ill to stand, you would use certain positions and projections. A pneumoperitoneum is the presence of air or gas in the peritoneal cavity, which is typically indicated in radiographic exams. The suitable positions in this case would be the left lateral decubitus and dorsal decubitus positions. In the left lateral decubitus position, the patient lies on their left side, which allows free air to rise and become visible at the highest point of the abdominal cavity, next to the abdominal wall. The dorsal decubitus position requires the patient to lie flat on their back (supine). A horizontal beam lateral view would be the required projection for this position to visualize air underneath the abdominal wall.