已知正方体ABCD﹣A₁B₁C₁D₁的棱长为1，以顶点A为球心，$\frac{2\sqrt{3}}{3}$为半径作一个球，则球面与正方体的表面相交所得到的曲线的长等于____ ．

我会读短文，回答问题。

春天的田野真美啊！柳树发芽了。桃树开了花。青青的小草悄悄地从地里钻出来，地上像插遍了密密的松针。金黄的油菜花，引得蜜蜂来回地飞舞。

    Now people are very concerned about the food problem. Steve Wilson prefers organic fruit, delivered right to the doorstep. He is willing to pay for it. If this is not possible, the 30-year-old computer technician will spend the extra money at the supermarket to buy organic food.

    “Organic product is always better,” Wilson said. “The food is free of pesticides(农药), and you are generally supporting family farms instead of large farms. And more often than not that it is locally grown and seasonal, so it is more tasty.” Wilson is one of the growing number of shoppers buying into the organic trend, and supermarkets across Britain are counting on more like him as they grow their organic food business. But how many shoppers really know what they are getting, and why are they willing to pay a higher price for organic product? Market research shows that Wilson and others who buy organic food can generally give clear reasons for their preferences—but their knowledge of organic food is far from complete. For example, small amounts of pesticides can be used on organic products. And about three quarters of organic food in Britain is not local but imported(进口)to meet growing demand. “The demand for organic food is increasing by about one third every year, so it is a very fast-growing market,” said Sue Flock, a specialist in this line of business.