Sphere

A sphere is a three-dimensional shape that is perfectly round, like a ball. It is shaped like a circle in 3D space. All points on the surface of a sphere are equally far from the center point. The distance from the center of the sphere to any point on the surface is called the radius.

Key Terms:

• Sphere: A three-dimensional shape that is perfectly round.
• Radius: The distance from the center of the sphere to any point on the surface.
• Diameter: The distance across the sphere passing through the center, which is twice the length of the radius.
• Volume: The amount of space inside the sphere.

Formulas:

• Volume of a Sphere: V = (4/3)πr³
• Surface Area of a Sphere: A = 4πr²

Examples:

Let's consider a sphere with a radius of 5 units.

1. Find the diameter:

       Diameter = 2 * Radius = 2 * 5 = 10 units
       

2. Find the volume:

       V = (4/3) * π * (5)³ = (4/3) * π * 125 = 523.6 cubic units
       

3. Find the surface area:

       A = 4 * π * 5² = 4 * π * 25 = 314.2 square units
       

Practice Questions:

1. Find the radius of a sphere with a diameter of 12 units.
2. Calculate the volume of a sphere with a radius of 3 units.
3. What is the surface area of a sphere with a radius of 6 units?

By understanding the concept of a sphere, its properties, and the related formulas, you will be able to solve problems involving spheres with confidence.