Find the volume generated when the region bounded by \(y=x\), the x-axis, and the lines \(x=0\) and \(x=2\) is rotated through \(360^\circ\) about the x-axis.

Find the volume generated when the region bounded by \(y=x^2\), the x-axis, and the lines \(x=0\) and \(x=1\) is rotated through \(360^\circ\) about the x-axis.

Find the volume generated when the region bounded by \(y=3x\), the x-axis, and the lines \(x=0\) and \(x=2\) is rotated through \(360^\circ\) about the x-axis.

Find the volume generated when the region bounded by \(y=2-x\), the x-axis, and the lines \(x=0\) and \(x=2\) is rotated through \(360^\circ\) about the x-axis.

Find the volume generated when the region bounded by \(y=\sqrt{x}\), the x-axis, and the lines \(x=0\) and \(x=4\) is rotated through \(360^\circ\) about the x-axis.