Is the verb "cast" in acting, metalworking and programming the same verb?

Question

• An actor is "cast" in a role: Jane Lee is cast as "Jo Smith".
• A sculpture is "cast" in bronze: molten bronze is poured into a mould.
• A variable is "cast" as a certain type of information in programming: is 1 the number one, or a string consisting of the character '1'? You "cast" it to resolve that problem.

Are these all the same verb at the root?

Here are the relevant verb definitions from Oxford Dictionaries Online:

1 [usually with adverbial of direction] chiefly literary Throw (something) forcefully in a specified direction: he cast the book down on to the chair angrily the fishermen cast a large net around a school of tuna figurative individuals who do not accept the norms are cast out from the group

4 Shape (metal or other material) by pouring it into a mould while molten: when hammered or cast, bronze could be made into tools

4.2 Arrange and present in a specified form or style: he issued statements cast in tones of reason

[unnumbered, noun] The actors taking part in a play, film, or other production: he draws sensitive performances from his inexperienced cast

Here's a definition from Merriam-Webster Learner's Dictionary for cast as a verb in relation to actors:

4 a : to assign roles for (a play, movie, etc.) to actors. cast a play
b : to assign (an actor or actress) a role in a film, play, etc. She was cast as a college professor who becomes a spy.

Answer 1

Cast is a prolific term with tens of different meanings, the root appears to be the same one:

• c. 1200, "to throw, fling, hurl," from a Scandinavian source akin to Old Norse kasta "to throw" (cognate with Swedish kasta, Danish kaste, North Frisian kastin), of uncertain origin.

• Meaning "to form in a mold" is late 15c. In the sense of "warp, turn" it replaced Old English weorpan (see warp (v.)), and itself largely has been superseded now by throw, though cast still is used of fishing lines and glances. Meaning "calculate, find by reckoning; chart (a course)" is from c. 1300.

• The sense of "a throw" carried an idea of "the form the thing takes after it has been thrown," which led to widespread and varied meanings, such as "group of actors in a play" (1630s).

• OED finds 42 distinct noun meaning and 83 verbal ones, with many sub-definitions. Many of the figurative senses converged in a general meaning "sort, kind, style" (mid-17c.). A cast in the eye (early 14c.) preserves the older verbal sense of "warp, turn."

(Etymonline)