The Sphere

A sphere is a three-dimensional shape that is perfectly round, with all points on its surface equidistant from its center. It is a type of round geometric shape that is similar to a ball. The surface area of a sphere is 4πr², where r is the radius of the sphere, and the volume of a sphere is (4/3)πr³.

Properties of a Sphere:

• Surface Area: The total area of the outer surface of a sphere is given by the formula 4πr², where r is the radius of the sphere.
• Volume: The space occupied by a sphere is given by the formula (4/3)πr³, where r is the radius of the sphere.
• Center: The center of a sphere is the point inside the sphere that is equidistant from all points on the surface.
• Diameter: The distance across a sphere through its center, which is twice the length of the radius.
• Circumference: The distance around the outer edge of the sphere is not defined, as a sphere does not have edges or corners.

Study Guide:

1. What is a sphere?
2. What is the formula for the surface area of a sphere?
3. What is the formula for the volume of a sphere?
4. What is the center of a sphere?
5. What is the diameter of a sphere?
6. Is the circumference of a sphere defined? Why or why not?

Understanding the properties of a sphere and being able to calculate its surface area and volume is important in various fields such as mathematics, physics, and engineering.