Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.

(a) A region that, when revolved around the x-axis, has both disk and washer cross sections.

(b) A region that, when revolved around the y-axis, has both disk and washer cross sections.

(c) A solid of revolution for which it is not possible to use
the disk or washer method.

A region that, when revolved around the x-axis, has both disk and washer cross sections

Consider the region $y=\frac{1}{2}\sqrt{x}$.

If it is revolved around x-axis, then it will disk shape.

Similarly consider the region between $y=\frac{1}{2}\sqrt{x}andy=\sqrt{x}$

When it is revolved around x-axis, then it will given washer shape.

Consider the region of the parabola, $y=\frac{1}{2}{x}^2$

If it is revolved around y-axis, then it will disk shape.

Similarly consider the region between$y=\frac{1}{2}{x}^{2}andy=x^2$

When it is revolved around x-axis, then it will given washer shape.

From the given information, the equation of the curve should be of the form $x=f\left(y\right)$.

Consider the equation where it is not possible or may not be easy.

$y=(x-1){(x-2)}^2$

in which it may not be possible to write equation in the form of yand the volume cannot be find using disk or washer methood.