The characteristics of a solid of revolution of a sphere include:
1. Symmetry: When a sphere is revolved around an axis, it creates a solid with perfect symmetry. This means that every point on the surface of the solid is equidistant from the axis of rotation.
2. Volume: The solid of revolution of a sphere has a volume that can be calculated using the formula for the volume of a sphere, which is \( V = \frac{4}{3} \pi r^3 \), where \( r \) is the radius of the sphere.
3. Surface Area: The surface area of the solid of revolution of a sphere can be determined by revolving the surface area of a hemisphere (half of a sphere) around an axis. The formula for the surface area of a sphere is \( A = 4 \pi r^2 \), where \( r \) is the radius of the sphere.
4. Cross-Section: The cross-section of the solid of revolution of a sphere perpendicular to the axis of rotation will be a circle. As you move along the axis, the size of the circle may change depending on the distance from the axis.
These characteristics help in understanding and visualizing the properties of solids of revolution created by rotating a sphere around an axis.
