题目

Planetary changes which will have an influence on many are drawing near because of the poor ecological (生态的) state of the planet. Actually change has already begun through climate changes, but most humans haven’t noticed this yet. Climate change has begun to influence the world already and will begin to worsen within the next few years. Around 2020 most people will begin to see that the results of climate change will be far more serious than now understood. As the planet is under big geological (地质的)stresses, which are continuously increasing, it will in the future no longe甲同学从一个半径为r的半圆形铁板中截取一块矩形ABCD，记其最大面积为S甲，乙同学从一个半径为R的圆形铁板中截取一块矩形EFGH，记其最大面积为S乙，试问r和R满足什么关系时，S甲=S乙？说明理由．