Eruvin 14B

במים״⁠ — במי מקוה. ״כל בשרו״⁠ — מים שכל גופו עולה בהן, וכמה הן? אמה על אמה ברום שלש אמות. ושיערו חכמים, מי מקוה ארבעים סאה.

in water; specifically in the water of a mikveh. The expression “all his flesh” (Leviticus 15:16) teaches that one must immerse in water that his whole body can enter at once. And how much is that? A cubit by a cubit by the height of 3 cubits. And the rabbis calculated that the volume of water necessary for a mikveh of this size is 40 se’a.

כמה הוו להו? חמש מאה גרמידי, לתלת מאה ⁠— מאה, למאה וחמשין ⁠— חמשין. בארבע מאה וחמשין סגיא!

The Talmud now calculates how many ritual baths should have been contained in Solomon’s Sea. The volume of the sea was 500 cubic cubits, as it was 10 cubits in length, 10 cubits in width, and 5 cubits in height. The minimum volume of a mikveh is 3 cubic cubits. Therefore, 300 cubic cubits is the volume of 100 ritual baths, and 150 cubic cubits is the volume of another 50 ritual baths. Consequently, 450 cubic cubits are enough to contain 150 ritual baths; but the volume of the sea was 500.

הני מילי בריבועא ⁠— ים שעשה שלמה עגול היה.

The Talmud answers that there is an error in the calculation: These calculations with regard to the volume of the sea would apply to a square, but the sea fashioned by Solomon was round, and its volume was therefore smaller.

מכדי, כמה מרובע יתר על העגול? רביע. לארבע מאה ⁠— מאה, למאה ⁠— עשרים וחמשה. הני מאה ועשרים וחמשה הוו להו!

The Talmud continues to ask: Now, how much larger is a square of 10-by-10 cubits than a circle with a diameter of 10 cubits? 1/4th. Consequently, 400 cubic cubits of our original calculation must be reduced to 300, which is the volume of 100 ritual baths; and the remaining 100 cubits must be reduced to 75, which is the volume of 25 ritual baths. According to this calculation, Solomon’s Sea was the size of only 125 ritual baths, not 150 as stated above.