1. Find the volume of the solid obtained by rotating the region bounded by \(y=x^3, y=8\) and the y-axis about the y-axis. solution

2. Find the volume of the solid generated by rotating the region enclosed by the curves \( y=x\) and \( y=x^2\) about the y-axis. solution

3. What is the volume of the solid generated by rotating the
region bounded by the curves \( y^2=x \) and \( y=2-x\) about the
y-axis? solution

4. Find the volume of the solid obtained by rotating the region bounded by \(y=x\) and \(y=x^2\) about the line \( y=-2\). solution

5. Find the volume of the solid obtained by rotating the region bounded by \(y=x\) and \(y=x^2\) about the line \( x=-1\). solution

6. Find the volume of the solid obtained by rotating the region bounded by the curves: \( y=\sqrt{x+2}\) and \( y=x\); axis of rotation: x-axis. solution

7. Find the volume of the solid obtained by rotating about the line \(x=-2\),
the region bounded by \(y=x\) and \(y=x^2\). solution

8. Find the volume of the solid obtained by rotating the region bounded by the curves \( y=8x^3, \, y=0, \,x=1 \) about the line \(x=2\). solution