The correct answer is: A. will be built
The sentence is in the future tense, so the correct verb form is “will be built.” The other options are not in the future tense.
Option B, “would be build,” is in the past subjunctive mood. The past subjunctive mood is used to express unreal or hypothetical situations. In this case, the situation is not unreal or hypothetical, so the past subjunctive mood is not appropriate.
Option C, “is built,” is in the present tense. The present tense is not appropriate for this sentence because it does not express a current or ongoing action.
Option D, “builds,” is in the third person singular present tense. The third person singular present tense is not appropriate for this sentence because the subject is “a new hospital,” which is a singular noun. The correct verb form for a singular noun in the future tense is “will be built.”