Newell needed a moderately simple mathematical model of a familiar object for his work. His wife Sandra Newell suggested modelling their tea service since they were sitting down to tea at the time. He got some graph paper and a pencil, and sketched the entire teapot by eye. Then he went back to the lab and edited bézier control points on a Tektronix storage tube, again by hand.
The teapot shape contains a number of elements that made it ideal for the graphics experiments of the time: it is round, contains saddle points, has a genus greater than zero because of the hole in the handle, can project a shadow on itself, and looks reasonable when displayed without a complex surface texture.
The real teapot is noticeably taller than the computer model because Newell's frame buffer used non-square pixels. Rather than distorting the image, Newell's colleague Jim Blinn reportedly scaled the geometry to cancel out the stretching, and when the model was shared with users of other systems, the scaling stuck. Height scale factor was 1.3.
The original, physical teapot was purchased from ZCMI (a department store in Salt Lake City, Utah) in 1974. It was donated to the Boston Computer Museum in 1984 where it was on display until 1990. It now resides in the ephemera collection at the Computer History Museum in Mountain View, California where it is catalogued as "Teapot used for Computer Graphics rendering" and bears the catalogue number X00398.1984.
With the advent first of computer generated short films, and then of full length feature films, it has become something of an in-joke to hide a Utah teapot somewhere in one of the film's scenes. For example, in the movie Toy Story the Utah teapot appears in a short tea-party scene.