The region bounded by f(x) = -3x^2 + 18x + 21, x = 0, and y = 0 is rotated about the y-axis. Find the volume of the solid of revolution. Find the exact value; write the answer without decimals.
2. Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on the right by the graph of g(y) = 2√y and on the left by the y-axis for 0 ≤ y ≤ 3, about the x-axis. Round your answer to the nearest hundredth position.
3. Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y = x^2, y = 0, and x = 2, about the y-axis.
4. Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on the right by the graph of g(y) = 7/y and on the left by the y-axis for 1 ≤ y ≤ 9, about the x-axis. Round your answer to the nearest hundredth position.