What was the Mechonah?
Radak: It was a base for the Kiyor (laver from which the Kohanim washed their hands and feet), like Moshe made (commanded to make) - "Es ha'Kiyor v'Es Kano" (Shemos 39:39). Malbim - after Shlomo made 10 lavers, he made 10 bases for them.
Did the Kiyor fill the width of the Mechonah?
Malbim: No. Verse 38 says that each Kiyor was 40 Bas, and it was four Amos. If it were four by four Amos wide, it would not be even one Amah tall 1 ! Rather, the Kiyor's height was four Amos, and if it was circular, the diameter was [about] one and three quarters Amah. Had it been square (and the side was one and three quarters), a height of three Amos would suffice [to make its volume 40 Bas]. Since a circle has only three quarters of the area of the square [around it], it needed to be four Amos tall. I will explain that the bottom was square. If so, we must say that it was one and three quarters from the outside; the added area of the square compensates for the area lost due to the thickness of the walls. The Mechonah was much wider, i.e. four by four.
For it was nine cubic Amos (three times the Shi'ur of a Mikveh).
What was three Amos tall?
Rashi: The Mechonah itself was one and a half Amos, and it rested on a base of one and a half Amos.
What shape was the Mechonah?
Rashi: The top half Amah was circular - "Chetzi ha'Amah Komah Agol Saviv" (verse 35). The bottom Amah was square.