find the volume of the solid formed when the region is revolved around the y axis
To find the volume of the solid formed when a region is revolved around the y-axis, we can use the disk method. The formula for the volume of a solid formed by revolving a region around the y-axis is:
V = π[∫(upper function)^2 - (lower function)^2] dy
Where the limits of integration are the y-values of the points of intersection of the upper and lower functions.
1. First, determine the upper and lower functions of the region.
2. Then, find the points of intersection by setting the upper and lower functions equal to each other and solve for y.
3. Finally, substitute the upper and lower functions into the volume formula and integrate with respect to y over the limits of integration.
If you provide the equations of the upper and lower functions or describe the region, I can help you calculate the volume of the solid formed when the region is revolved around the y-axis.