There also is every possibility that the college's notion of what you need is will be different from what your family thinks it is. Depending on the scholarship pay-out rules, and the college's aid policy, that scholarship might be to your advantage. For example, if outside money can be used to replace loans in your aid package, then you could use a student loan to help cover part of what your family needs to pay.
Apply for that scholarship. You aren't going to know your aid packages until April or May, and when you do have those aid offers in hand, that scholarship might make a difference.