The membrane of the vacuole that surrounds the material and fuses with the cell membrane is called the tonoplast. This membrane plays a crucial role in the storage and regulation of substances within the vacuole.
When a vacuole is full and needs to release its contents, the tonoplast fuses with the cell membrane. This process is essential for various cellular mechanisms, such as exocytosis, where substances are expelled from the cell. The tonoplast is selectively permeable, allowing the cell to maintain homeostasis by controlling what enters and exits the vacuole.