The institution of the sacrament is one of the last things that Christ did on day #1 of his visit. The events of 3 Nephi 11-18 likely consumed most of the day. Although they had been fed an unbelievable spiritual feast, the bread and wine given on this occasion were the only physical food eaten during Christ's visit. On four separate occasions, the record states that they 'were filled' (v. 4,5,9). We should not assume, because our sacrament comes in little cups with small pieces of bread, that their portions were just as small. The record says they were filled, and that is how we should understand it.
In fact, the symbolism is more beautiful if they were physically filled. As in so many other gospel symbols, the physical becomes a type for the spiritual. As physical hunger and thirst can only be satisfied with food and drink, so the soul that hungers and thirsts after righteousness can only be filled with the Holy Ghost (3 Nephi 12:6). Therefore, the Nephites must have been filled both physically and spiritually.
Jeffrey R. Holland
"We no longer include a supper with this ordinance, but it is a feast nevertheless. We can be fortified by it for whatever life requires of us, and in so doing we will be more compassionate to others along the way." (Conference Report, Oct. 1995, "This Do in Remembrance of Me")
Melvin J. Ballard
"We must come, however, to the sacrament table hungry. If we should repair to a banquet where the finest of earth's providing may be had, without hunger, without appetite, the food would not be tempting, nor do us any good. If we repair to the sacrament table, we must come hungering and thirsting after righteousness, for spiritual growth." ("The Sacramental Covenant," Improvement Era, October 1919, pp. 1025)