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NEW YORK—Corn prices fell for the second straight session Tuesday on relief over news that farmers planted more corn this year than traders expected.

Soybeans, however, reached another record high. Monday’s crop report from the U.S. Department of Agriculture showed that while corn acreage was higher than anticipated, the number of acres planted with soybeans was smaller.

Commodities prices—from corn and soybeans to crude oil and gasoline—have been soaring this year due to supply concerns, as well as the tumbling U.S. dollar. When the dollar is weak, the dollar-denominat...