his spare time is made full use( )law.(of studing/of to study).

选 of to study.
原因：
短语：
从分利用某人的业余时间(为了/来)做某事
make full use of one's time to do sth
变为被动语态就是：
one's spare time is made full use of【 to do sth 不定式,作目的状语】
其中,介词of 的宾语,就是前面的his spare time.
祝你开心如意!