Did Chazal know the value of Pi?

Todays daf (Bava Basra 14) strongly suggests that they did not. The Gemara is discussing the size of the Aron and what was in it.

The Gemara states the following facts:

1. The Aron was 15 tefachim wide
2. Half a Tefach on each side was the width of the wall, therefore the Aron had 14 tefachim of usable space
3. The luchos were 6x6 so the 2 luchos in the Aron took up 12 tefachim of space
4. The Sefer Torah that Moshe wrote was placed in the leftover 2 tefachim in the Aron
5. The ideal size of a Sefer Torah is 
1. 6 tefachim height
2. 6 tefachim circumference of the parchment rolls with 3 tefachim on each side
6. The ratio of circumference to diamter is 3:1
7. Based on the above (5 and 6) the width of the Sefer Torah would be 2 tefachim

The Gemara asks based on the above facts, that since the Sefer Torah fits exactly in the space leftover (2 tefachim) how would they take the Torah in and out of the Aron? 

However, the Gemara's question only makes sense if you assume a ratio of 3:1 between circumference and diameter (as stated above 6), however, in reality the ration is Pi(3.14):1 which means that the width of the Torah would only be 1.91 tefachim which would leave some space to take it in or out. Therefore, it is clear that Chazal did not the value of Pi otherwise the Gemara's question makes no sense. In fact, Tosafos in Eruvin (14b) asks this question.

For many people, the above is not a problem, Chazal were not scientists and used the generally available knowledege of their time and therefore made mistakes in science. However, the Charedi world has rejected this position and claim that Chazal received their science from Heaven and  never made mistakes in science inclusing the fact that Pi is irrational (see http://www.rationalistjudaism.com/2016/06/is-it-amazing-that-rambam-knew-that-pi.html). This Gemara seems to clearly contradict that view.

One additional noteworthy point is that we see clearly that Chazal did not have a mesora about things like the Aron and the Luchos. R' Yehuda and R' Meir have a dispute as to both the size of the Aron and whether Moshe's sefwer torah was inside teh aron or not. Likewise the Yerushalmi argues with the Bavli over the size of the luchos, Bavli 6x6, Yerushalmi 6x3. If Chazal didn't have a mesora about things like the Aron and teh Luchos then what did they have a mesora on?