The correct passive form of the given sentence is:

☀ An amphitheatre will be built by the government.

So, the correct passive form is: "An amphitheatre will be built by the government."

The other options and their explanations:

☀ An amphitheatre will be build by the government.

• This option is not grammatically correct. The correct past participle form of "build" is "built," not "build."

☀ An amphitheatre would be built by the government.

• This option uses "would be" instead of "will be," which changes the meaning of the sentence to a conditional statement. It suggests that the government might build the amphitheatre, but there is some condition or uncertainty involved.

☀ An amphitheatre be build by the government.

• This option is not grammatically correct. In the passive voice, we use "be" with the past participle, but it needs the auxiliary verb "will" to indicate the future tense. The correct form is "will be built."