# How Much Did the Teivah Weigh?

#### V’zeh asher ta’aseh osah shalosh me’os amah orech ha’teivah chamishim amah rach’bah u’sheloshim amah komasah (Bereishis 6:15)

Parashas Noach revolves around the flood that Hashem brought to destroy the earth. In order to save Noach, his family, and all of the species of birds and animals, Hashem commanded Noach to make an ark that would measure 300 cubits long, 50 cubits wide and 30 cubits tall. One year, on a 12th-grade Chumash test, Harav Moshe Heinemann of Baltimore asked the students to determine the weight of the ark. He did not ask them to calculate the actual weight, but rather to detail how one would go about computing it.

The first key to answering this question lies in the words of Rashi, who writes (8:4) that based on the rate at which the floodwaters receded, we can conclude that the ark was submerged 11 cubits in the water. The second necessary component for this calculation is the Principle of Flotation, which is derived from Archimedes’ principle. The Principle of Flotation states that the weight of an object floating in a liquid is equal to the weight of the liquid that it displaces. In our case, multiplying the dimensions of the ark specified by the Torah by the depth of water in which it was submerged (300 x 50 x 11) yields a total water displacement of 165,000 cubits3.

Converting this into contemporary measurements is subject to a dispute regarding the exact length of a cubit. The two primary opinions are those of the Chazon Ish and Harav Avraham Chaim Naeh; there is a third opinion, that of Harav Moshe Feinstein, which falls in the middle. Their disagreement about the size of a cubit will result in a corresponding difference of opinion regarding the amount of water displaced by the ark, and its resulting weight. According to the Chazon Ish, a cubit is 22.7 inches, in which case one cubit3 is 6.77 cubic feet, and the total amount of water displaced by the ark was 1,117,050 feet3 (165,000 x 6.77). According to Harav Avraham Chaim Naeh, a cubit is only 18.9 inches, in which case one cubit3 is 3.91 cubic feet, and the total amount of water displaced by the ark was 645,150 feet3 (165,000 x 3.91).

Now that we know how much water was displaced by the ark, if we calculate the weight of the water, Archimedes’ principle tells us that the ark weighed the same amount. Sea water is slightly denser than fresh water, and it weighs approximately 64 pounds per cubic foot. Although this figure changes under extreme temperature variation, and the Gemara (Rosh Hashanah 12a) teaches that the floodwaters were boiling during the 40 days of the flood, Rashi’s calculation is based on the rate at which the water receded during the 150 days that followed the flood, at which time the water had presumably cooled to a more normal temperature.

As such, based on the weight of 64 pounds per cubic foot, the total weight of Noach’s ark (with its contents) according to the Chazon Ish was 71,482,176 pounds, or 35,741 tons. According to Harav Avraham Chaim Naeh, it weighed 41,257,728 pounds, or 20,629 tons. For comparative purposes, the Titanic weighed 46,328 tons, although it was 883 feet long, while Noach’s ark was approximately 500-550 feet in length. Whether any of the students in Harav Heinemann’s class came up with this analysis is unclear.

Q: The Gemara in Bava Kamma (91b) derives from Bereishis 9:5 that it is forbidden to injure one’s body. Does having plastic surgery for cosmetic reasons violate this prohibition?

A: In the case of a woman who wanted to have plastic surgery to improve her appearance, Harav Moshe Feinstein ruled that it is permissible. He quotes the Rambam (Hilchos Choveil U’Mazik 5:1), who specifies that the Torah prohibition against injuring a person (including oneself) only applies when it is done maliciously and degradingly, which is not the case in a surgical procedure.

Even if one disagrees with this distinction, Rav Moshe permits the surgery due to the fact that it is being done willingly and for the well-being of the woman. This is also the opinion of the Chelkas Yaakov. In the case of a woman who felt that her unattractive nose diminished her chances of marrying and wanted to have it surgically altered, Harav Menashe Klein cites Talmudic sources indicating that medical procedures were performed at that time to improve appearance, thereby proving their permissibility.

He adds that it is forbidden for a man to undergo surgery solely to enhance his looks, as attempting to beautify himself in this manner violates the prohibition against adopting female garb and conduct (Devarim 22:5). However, if his appearance causes him such discomfort that he avoids interacting with others, surgery would then be permissible.

Dayan Yitzchak Yaakov Weiss agrees that cosmetic surgery does not violate the prohibition against injuring oneself, but he is hesitant to permit any elective surgery due to the inherent risk involved, and he concludes that the subject needs further study. On the other hand, Harav Eliezer Waldenberg strongly prohibits all cosmetic surgery. He argues that it is forbidden both for the doctor, who is only given permission by the Torah to heal sick patients but not to perform unnecessary procedures on healthy people, and for the patient, who has no right to ask the doctor to wound him simply to enhance his appearance.

Additionally, on a theological level, he maintains that plastic surgery is an insult to Hashem, implying that He created a person defectively and incorrectly.

Harav Shlomo Zalman Auerbach permits cosmetic surgery if it is being done to remove a blemish that causes a person psychological suffering and embarrassment, but forbids elective procedures that are done solely to enhance one’s appearance. For practical questions, one should consult a competent Rabbinical authority.

Originally from Kansas City, Rabbi Ozer Alport graduated from Harvard, learned in Mir Yerushalayim for five years, and now lives in Brooklyn, where he learns in Yeshivas Beis Yosef, is the author of the recently-published sefer Parsha Potpourri, and gives weekly shiurim. To send comments to the author or to receive his Divrei Torah weekly, please email oalport@Hamodia.com.