Final answer:
The volume of the solid can be found by calculating the area of each cross-section, which in this case is a semicircle, and adding them up. The formula for the area of a circle is used to find the area of each cross-section, and then integration is used to find the volume. The volume of the solid is found to be 3.2π.
Step-by-step explanation:
The volume of the solid can be found by calculating the area of each cross-section and then adding them up. Since each cross-section is a semicircle, we can find the area by using the formula for the area of a circle, multiplied by 1/2.
The formula for the area of a circle is A = πr², where r is the radius. In this case, the radius is equal to the y-coordinate of the curve y = x². So, the area of each cross-section is A = (π/2) * (x²)² = (π/2)x⁴.
To find the volume, we integrate the area function from x = 0 to x = 2: V = ∫[0,2] (π/2)x⁴ dx = (π/2)(1/5)x⁵]_[0,2] = (π/2)(1/5)(2⁵ - 0⁵) = 16π/5 = 3.2π.