General Polk, in my opinion, was killed by the second volley fired from the first battery referred to.
In a conversation with General Johnston, after the war, he explained that on that day he had ridden in person from Marietta to Pine Mountain, held by Bates's division, and was accompanied by Generals Hardee and Polk.

When on Pine Mountain, reconnoitring, quite a group of soldiers, belonging to the battery close by, clustered about him.

He noticed the preparations of our battery to fire, and cautioned these men to scatter.

They did so, and he likewise hurried behind the parapet, from which he had an equally good view of our position but General Polk, who was dignified and corpulent, walked back slowly, not wishing to appear too hurried or cautious in the presence of the men, and was struck across the breast by an unexploded shell, which killed him instantly.

This is my memory of the conversation, and it is confirmed by Johnston himself in his "Narrative," page 337, except that he calculated the distance of our battery at six hundred yards, and says that Polk was killed by the third shot; I know that our guns fired by volley, and believe that he was hit by a shot of the second volley.