Schottenfreude. "Fernsehturm" is the German word for television tower. "Fernsehen" means television, as in the noun, the electronic device. To break that down further, "sehen" means to see. The word "fern" means remote; as in at a distance. So You can string that together pretty sensibly "fern-sehen-term" or "remote - seeing - tower." But "turm" was the root that meant tower or steeple.
To further cloud this waters for those of use who speak a largely non-agglomerating language, "Fernmeldeturm" is the correct word, only if it's part of a building. The noun "meldung" means "information, report or an announcement. So they added the "building" root when it was just a tower and then further added the "information" after the tower was on a building. Tricky language. Also sometimes makes things difficult to research.
So I deduced that since the German word for radio is radio.. that radio tower should be then a radioturm. The answer is... sort of. Radioturm is not a popular word. It's used only in specific contexts, mostly much older radio constructions. Ex. Radioturm Schuchow, Radioturm mit Sirene, Shabolovka Radioturm, and the Shukhov radioturm which I wrote about previously.