Final answer:
The volume of the solid with equilateral triangular cross-sections between y=0 and y=2 is 2√3 cubic units.
Step-by-step explanation:
To find the volume of the solid described, we need to consider the shape and dimensions of the cross sections and the range over which they extend. The cross sections are equilateral triangles and the base of each triangle runs from one semicircle defined by x = -√(4-y²) to the other defined by x = √(4-y²). Since these are semicircles, the base of each triangle, or the diameter of the semicircle, ranges from x = -2 to x = 2 for any value of y between 0 and 2. The side length (s) of an equilateral triangle is the same as its height, so the area (A) of each cross section can be computed using the formula A = √3/4 × s², and the side length is s = 2 because this is the diameter of the semicircle.
From the given range for y, we know the height (h) of the solid (the distance between the two planes perpendicular to the y-axis) is 2. Using the formula V = Ah, we can find the volume by multiplying the cross-sectional area by the height. In this case, the volume is V = (√3/4 × 2²) × 2, or V = 2√3 cubic units.