Final answer:
The domain of the rectangle under the semicircle y = sqrt(36 - x²) is determined by the values of x, specifically within the interval [-6, 6].
The correct option is A.
Step-by-step explanation:
The domain of a rectangle that is bounded by the x-axis and the semicircle y = sqrt(36 - x²) is determined by the values of x. The semicircle's equation is derived from the circle equation x² + y² = 36, where the circle has a radius of 6.
Because we are dealing with a semicircle that lies above the x-axis, the domain of this shape will be the range of x-values for which the function y = sqrt(36 - x²) is defined, which corresponds to the interval [-6, 6].
The y-values are determined by the function itself for a given x-value within this domain. Thus, only the x-values define the horizontal span of the rectangle under the semicircle, which is also the domain of the rectangle.
The correct option is A.