Sphere

A sphere is a three-dimensional shape that is perfectly round, like a ball. It is defined as the set of all points in space that are a given distance (the radius) from a given point (the center).

Characteristics of a Sphere:

1. Surface Area: The surface area of a sphere is given by the formula 4πr², where r is the radius of the sphere.
2. Volume: The volume of a sphere is given by the formula (4/3)πr³.
3. Symmetry: A sphere has infinite rotational symmetry, meaning it looks the same from any angle of rotation.
4. Center: The point inside the sphere from which all points on the sphere are equidistant.

Examples of Spheres:

There are many real-life examples of spheres, such as:

• Marbles
• Planets
• Bubbles
• Balloons
• Baseballs and other sports balls

Study Guide:

When studying spheres, make sure to focus on the following key points:

1. Understand the definition of a sphere and its characteristics.
2. Be able to calculate the surface area and volume of a sphere using the correct formulas.
3. Practice identifying real-life examples of spheres.
4. Compare and contrast spheres with other three-dimensional shapes, such as cubes and cylinders.

Remember to use visual aids, such as models or diagrams, to help reinforce your understanding of spheres.