africanmasks said:you're rotating around the y not x
The formula for finding the volume of a solid in a y-axis rotation region is ∫(π * r^2)dx, where r is the distance from the y-axis to the outer edge of the solid and dx is the width of each infinitesimally thin slice of the solid.
The limits of integration for finding the volume in a y-axis rotation region are determined by the points at which the solid intersects with the y-axis. These points can be found by setting the equation of the solid equal to zero and solving for x.
No, the formula for finding the volume of a solid in a y-axis rotation region is specific to that particular region. Different formulas are used for finding the volume in other axis rotation regions, such as the x-axis or z-axis.
The shape of the solid greatly affects the volume in a y-axis rotation region. A solid with a larger radius will have a greater volume, while a solid with a smaller radius will have a smaller volume.
Yes, calculus is used to find the volume of a solid in a y-axis rotation region by using integration to sum up the infinitesimally thin slices of the solid and find the total volume.