Sphere

A sphere is a three-dimensional geometric 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, denoted as "r") from a given point (the center).

Formulas for a Sphere

The formula for the volume of a sphere is:

The formula for the surface area of a sphere is:

Key Concepts

1. Radius: The distance from the center of the sphere to any point on its surface.
2. Diameter: The distance across the sphere through the center, which is twice the radius (d = 2r).
3. Volume: The amount of space enclosed by the sphere.
4. Surface Area: The total area of the sphere's surface.

Example Problems

Problem 1: Find the volume and surface area of a sphere with radius 5 units.

Volume: \( V = \frac{4}{3} \pi (5)^3 = \frac{500}{3} \pi \) cubic units

Surface Area: \( A = 4 \pi (5)^2 = 100 \pi \) square units

Problem 2: If the diameter of a sphere is 10 cm, find its volume.

Since the diameter is 10 cm, the radius is \( \frac{10}{2} = 5 \) cm.

Volume: \( V = \frac{4}{3} \pi (5)^3 = \frac{500}{3} \pi \) cubic cm

Study Tips

1. Understand the difference between radius and diameter, and how they are related.
2. Memorize the formulas for volume and surface area of a sphere.
3. Practice using the formulas to solve various problems involving spheres.
4. Visualize real-life examples of spheres to better understand their properties.

By understanding the concepts and practicing problems, you'll be well-prepared to tackle any sphere-related questions!

[Sphere] Related Worksheets and Study Guides:

• Finding VolumeMathematics • Seventh Grade