Watch this animation to get an idea of cylindrical shells:

1. Find the volume of the solid generated by revolving the region
bounded by the curves \( y=\sqrt{x}, x=2\) and \( y=0 \) about the y-axis.
solution

2. Let R be the region bounded by the curves \(y=\sqrt[3]{x},
y=0\) and \( x=1\). Find the volume of the solid generated by revolving the region R about
the y-axis. solution

3. Find the volume of the solid generated by revolving the region bounded by the curves \( y=\sqrt{x},
y=2\) and \(x=0 \) about the x-axis.
solution

4. Find the volume of the solid generated by revolving
the region bounded by the curves \( y=\sqrt{x}, x=4\) and \(y=0 \) about the
the line \(y=-2\). solution

5. Find the volume of the solid obtained by rotating about the line \(
x = 2\), the region bounded by \(y=x^4, y=0\) and \( x=1\). solution

6. 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

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