Sphere

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

Characteristics of a Sphere

1. Radius: The distance from the center of the sphere to any point on its surface.
2. Diameter: The distance across the sphere through its center, which is twice the radius.
3. Surface Area: The total area of the outer surface of a sphere, given by the formula 4πr², where r is the radius.
4. Volume: The amount of space inside the sphere, given by the formula 4/3πr³.

Study Guide

Here are some key points to remember about spheres:

• Understand the concept of a sphere as a perfectly round three-dimensional object.
• Be able to calculate the radius, diameter, surface area, and volume of a sphere using the appropriate formulas.
• Practice solving problems involving spheres, such as finding the radius when given the surface area, or finding the volume when given the diameter.
• Identify real-life objects that can be represented by spheres, such as balls, planets, and bubbles.

Remember to use the formulas and concepts to solve problems and visualize the shape of a sphere in real-world scenarios.