1a. Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the given curve about the y-axis. Answer exactly or round to 2 decimal places.
y = 4 - (x - 8)^2.
1b. 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. Answer exactly or round to 2 decimal places.
1c. The region bounded by y = -2x^2 + 12x + 32, x = 0, and y = 0 is rotated about the y-axis. Find the volume of this solid of revolution: Find the exact value. Write your answer without using decimals.
1d. Find the volume of the solid obtained by rotating the region bounded by y = 2√x + 3, y = 3, y = 4, and x = 0, about the y-axis.