Why name Pyrex mixing bowls after Cinderella? 

'Cinderella bowl' is a well-known nickname for the type of nesting bowl with a handle on one side and a spout on the other.  This name has become a convenient way to differentiate it from the older style of nesting bowl with a completely round circumference.

Cinderella bowls, 441 & 444.  The large bowl is from a 1964 Chip & Dip set.
     
What is not well-known is that in the late 1950s when Cinderella bowls debuted*, many more opal and clear Pyrex items also would bear this same name.  In addition to the Cinderella Bowl Set (440 set) launched in 1957, the following new items would appear between 1958 and the early 1960s, and some of these are promotionals made for only one or two seasons:

Cinderella Butter Dish

Cinderella Beverage Server (8 cup carafe with candle warmer)

Cinderella Carafe (8 cup or 12 cup with candle warmers)

Cinderella Snack and Dip Set (025 & 410 square Hostess bowls and bracket)

Cinderella Electric Buffet (575 rectangular Space Saver & 12 cup carafe with electric warmer)

Cinderella Serving Casserole (575 rectangular Space Saver with cradle, or candle warmer cradle)

Cinderella Oval Open Baker (053 oval)

Cinderella Divided Serving Dish (063 oval)

Deluxe Cinderella Casserole (045 oval with candle warmer cradle)

Cinderella Serving Bowl (443 with candle warmer cradle)

Cinderella Twin Server Set (two 472s with cradle)

Cinderella New Buffet Twins (two 473s with cradle)

Cinderella Bake Serve and Store Set (470 set)

Cinderella Casserole Set (480 set)

A 410 and an 025 comprise the 1959 Cinderella Snack and Dip Set (bracket not shown).  This square bowl style had been introduced in 1949 in the form of Hostess Sets and Hostess Casseroles.
               
The Cinderella naming trend peaked in 1958, and a smaller selection of items was introduced with that name in 1959.  By the early 1960s just a few new items named Cinderella were appearing, and the existing ones like 440 bowls and 470/480 casseroles would drop the name entirely from advertisements and packaging by the mid 1960s.

(Photo: Pyrex carafe with gold-leaf decoration.  Image from brochure dating to about 1961.)

One example of a 575 2 Qt Space Saver.  With different patterns and the addition of cradles, this size and shape was sometimes called Cinderella too.  Conversely, the shallow Space Saver, a 548 1¼ Qt, never used the Cinderella name.

When 'Cinderella' has been applied arbitrarily to such a diverse range of casseroles and carafes, plus ovals, rounds, rectangles and squares, the meaning of the name clearly is unrelated to the shape or function of the piece.  Neither is it a descriptor of the style of the handles or spout since some of these items have no handles or spouts at all.

(Photo:  Cinderella Butter dish in Sandalwood, a Pyrex pattern from the early 1960s.)

The choice of the Cinderella name at that time coincides with the first re-release of the Disney animated film.  Although Cinderella originally opened in 1950, it was popular enough to make a return to theatres in the spring of 1957.  Also making an impact with the public was the televised Rodgers & Hammerstein musical by the same name, with Julie Andrews in the lead role.  The musical was written specifically for CBS, and it was broadcast live and in colour on March 31 1957.  The event earned record-breaking viewing figures, with about 25 million households tuning in.  Just weeks later on April 29 1957, NBC aired Prokofiev's Cinderella by the Royal Ballet, starring Margot Fonteyn.

In the context of the fairytale, slippers made of glass are emblematic of the main character's favourable rise in status.  This symbolism probably resonated with executives at Corning, a company at the forefront of the industry, whose history is synonymous with the greatest advancements in the capabilities of glass.

The lidless 053 Open Oval Baker is related to the 963/063 Divided Serving Dish.  Both have a 1½ Qt capacity. 

Currently 'Cinderella' has evolved into commonly accepted terminology for the 440 nesting bowls, mainly because they were the first Pyrex product to be named this way.  To a lesser extent the word is understood also as a reference to the round 470/480 casseroles, whose handles are shaped like the spout of a 440 bowl.


* - Cinderella bowls were introduced with three pattern/colour choices: turquoise Butterprint, pink Gooseberry, yellow & black Gooseberry.  The shape of the Cinderella bowl was designed by John Phillip Johnson.

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1961 Pyrex Package Leaflet
When was that Pyrex pattern or piece introduced?