这是关于A of B, 谁修饰谁的问题。有点类似 a number of people 和 the number of people, 前者是A修饰B,后者B修饰A。
第一句的the amount of food 是B修饰A, want的是amount, 不是food。好比,I want to know the weight of an elephant.
第二句是A修饰B, 类似你说, eat this amount of food / that much of food / a lot of food,等
两个都是量的意思,food是食物的意思