The sentence that requires semicolons instead of commas is the first one:
"A well-balanced diet includes root vegetables, such as carrots, dark red fruits, such as strawberries, and whole grains, such as brown rice."
In this case, semicolons would help to clearly separate the items in the list, especially since each item includes additional details (the examples following "such as").
Corrected with semicolons, it would read:
"A well-balanced diet includes root vegetables, such as carrots; dark red fruits, such as strawberries; and whole grains, such as brown rice."