student93 said:
Draw a graph and select a disk, it becomes clear why the outer radius is that.student93 said:
Yes. :)
A solid of revolution is a three-dimensional figure formed by rotating a two-dimensional shape around an axis. The resulting figure is symmetrical and has a circular cross-section.
The volume of a solid of revolution can be found by using the formula V = π ∫ (R(x))^2 dx, where R(x) represents the radius of the cross-section at a given point along the axis of rotation.
The disk method involves slicing the solid into thin disks and adding up the volumes of each disk, while the shell method involves slicing the solid into thin cylindrical shells and adding up the volumes of each shell. The method used depends on the shape of the cross-section and the axis of rotation.
The limits of integration can be determined by identifying the points of intersection between the curve and the axis of rotation. These points will be used as the upper and lower limits of integration.
No, the volume of a solid of revolution cannot be negative as it represents a physical quantity and cannot have a negative value. If a negative value is obtained, it is likely due to an error in the calculations.
