Final answer:
The Niobid Krater was made out of clay using the red figure technique and falls under the category of terracotta pottery, popular in ancient Greece for its durability and workability.
Step-by-step explanation:
The Niobid Krater, a classical piece from around 460 - 450 BCE attributed to the Niobid Painter, is made using the red figure technique, a technique where figures are left in the natural red color of the clay while the background is painted black. The material used for the Niobid Krater is clay, option 2 from your choices. Given its function as a calyx-krater, which is a vessel used for mixing wine and water, terracotta, a type of fired clay, was commonly used for such ceramics in ancient Greece. Terracotta is known for its durability, workability, and ability to hold intricate details, making it an excellent choice for the detailed scenes found on red-figure pottery.
Other notable examples of similar pottery in this era also use terracotta, such as the column-krater and kangaroos. It's noteworthy that while other materials such as marble were typically reserved for sculpture, and bronze for other types of artwork, terracotta was the material of choice for functional pottery like kraters and oinochoai.