The Shell Method Worksheet with Answer Key

What's on the worksheet

1. The region between the parabolas y = x² and y = 5x - x² is revolved about the y-axis.
2. The region under y = 2√(x² + 36) and above the x-axis for 0 ≤ x ≤ 8 is revolved about the y-axis.
3. The region between y = x² and y = x³ for 0 ≤ x ≤ 1 is revolved about the line x = 4.
4. The region bounded by the parabola x = y² and the line x = 4 is revolved about the line y = -5.
5. Let R be the region bounded by y = √(x), the line y = x - 2 and the x-axis.
6. Each region lies under the given curve and above the x-axis, for all x ≥ 0, and is revolved about the y-axis.
7. Let S be the region between y = x² and y = x + 6.