Explanation

We have two circles, and we need to find the radius of the smaller one. The circumference, area, or radius of either the larger or smaller circle will be sufficient to do so. On to the statements, separately first.

Statement (1) tells us that the radius of the garden is 5. The radius of the well is that of the garden, so the radius of the well is 1, and the area of the mouth of the well is . We have answered the question definitively, so Statement (1) is sufficient.

Statement (2) gives us the circumference of the larger circle. From it, we know that the circumference of the smaller circle is . Therefore, the radius of the smaller circle is 1 and the area is . We have answered the question definitively, so Statement (2) is sufficient. The correct answer is (D). Since various facts about a circle gives us its radius and the radius gives us all of those things in turn, Data Sufficiency questions involving circles tend toward sufficiency.

Again, the correct answer is (D).