What is a sphere? (definition and examples)

📚 What is a Sphere?

A sphere is a three-dimensional geometric shape that is perfectly round. All points on the surface of a sphere are equidistant from its center. Think of it as a 3D circle!

🔍 Definition: A sphere is the set of all points in three-dimensional space that are located at a fixed distance (the radius) from a given point (the center).

Quick Study Guide

📏 Radius (r): The distance from the center of the sphere to any point on its surface. 🟠 Diameter (d): The distance across the sphere passing through the center ($d = 2r$). 🧮 Surface Area (A): The total area of the outer surface of the sphere ($A = 4\pi r^2$). 📦 Volume (V): The amount of space enclosed by the sphere ($V = \frac{4}{3}\pi r^3$).

Practice Quiz

1. What is the defining characteristic of a sphere?
   1. It has flat sides.
   2. All points on the surface are equidistant from the center.
   3. It is a two-dimensional shape.
   4. It has corners.
2. What is the formula for the surface area of a sphere?
   1. $\pi r^2$
   2. $2\pi r$
   3. $4\pi r^2$
   4. $\frac{4}{3}\pi r^3$
3. What is the formula for the volume of a sphere?
   1. $4\pi r^2$
   2. $\pi r^2 h$
   3. $\frac{1}{3}\pi r^2 h$
   4. $\frac{4}{3}\pi r^3$
4. If the radius of a sphere is 3 cm, what is its diameter?
   1. 1.5 cm
   2. 6 cm
   3. 9 cm
   4. 3 cm
5. Which of the following is NOT an example of a sphere?
   1. A basketball
   2. A globe
   3. A pancake
   4. A marble
6. If the diameter of a sphere is 10 cm, what is its radius?
   1. 5 cm
   2. 10 cm
   3. 20 cm
   4. 3.14 cm
7. What happens to the volume of a sphere if you double its radius?
   1. It doubles.
   2. It quadruples.
   3. It increases by a factor of eight.
   4. It stays the same.