Explanation:
To find the volume of this solid, we will use the method of cylindrical shells. We will integrate the cross-sectional area of a cylinder, given by πr^2, over the height of the solid. The height of the solid is given by the difference between the upper and lower bounds of the region, which are y = x^2 and y = 0, respectively. The radius of each cylindrical shell is given by the distance of the cross-sectional circle from the y-axis, which is x.
So, the volume of the solid is given by the integral:
V = ∫[0, 1] π * x^2 dx
Using the antiderivative of π * x^2, which is π * x^3 / 3, we can find the definite integral:
V = (π * x^3)/3 from 0 to 1
Evaluating the definite integral and simplifying, we get:
V = π/3 units^3
So, the volume of the solid is π/3 units^3.