Question Use the washer method to calculate the volume of the solid formed when the region bounded by \( y=2 x^{2} \) and \( y=2 \), revolved around the the line \( y=3 \).

To visualize the washer method, imagine slicing our solid into thin disks, or "washers," perpendicular to the axis of rotation. The outer radius of each washer is determined by the distance from \( y=3 \) to \( y=2 \) (the upper curve), while the inner radius comes from \( y=3 \) to \( y=2x^2 \) (the lower curve). This gives us the formula for volume \( V = \pi \int_{-1}^{1} [(3-2)^2 - (3-2x^2)^2] \, dx \). In practice, this technique shines in engineering and physics where volume calculations are essential. For example, when creating components with curved surfaces, like pipes or tanks, engineers often need to know how much material to use or the space that will be filled with fluid. The washer method is a reliable way to ensure accurate volume calculations for complex shapes in those real-world scenarios!