Question

A fancy notepad has edges that follow the graphs of and . The notepad is 12 inches long and 1 inch thick.
Explain how you could use cross sections or slices cut perpendicular to the x-axis to find the volume of this notepad.

Answer 1

A fancy notepad has edges that follow the graphs of \[y=\frac{ 1 }{ 2 }\sin(x)-2\] and \[y=2-\frac{ 1 }{ 2 } \sin(x)\]. The notepad is 12 inches long and 1 inch thick.
Explain how you could use cross sections or slices cut perpendicular to the x-axis to find the volume of this notepad.

Answer 2

You can use integrals, and methods of revolution based on the shape of the pad (Shell, Disk, Washer.. Etc) to find the volume of the solid formed by the outlines of the "notepad".