Radius and Diameter
Radius and diameter are fundamental circle measurements taught in Grade 4 Saxon Math Intermediate 4 (Chapter 3). The radius is the distance from the center to the edge; the diameter is the full distance across through the center. The diameter always equals twice the radius: d = 2r, and r = d/2. For a pizza with radius 7 inches, the diameter is 14 inches. For a bike wheel with diameter 26 inches, the radius is 13 inches.
Key Concepts
Property The radius of a circle is the distance from the center to the edge. The diameter is the distance across the circle through the center. The diameter of a circle equals two radii.
Examples If a pizza has a radius of $7$ inches, its diameter is $2 \times 7 = 14$ inches. If the diameter of a bike wheel is $26$ inches, its radius is $26 \div 2 = 13$ inches.
Explanation Imagine a pizza! The radius is the length from the exact center to the yummy crust. The diameter is a straight cut all the way across the pizza that passes through the center point. Since that cut is made of one radius going from the center to the left and another to the right, the diameter is always twice as long!
Common Questions
What is the relationship between radius and diameter?
The diameter equals twice the radius: d = 2r. The radius equals half the diameter: r = d/2. The diameter is the longer measurement (all the way across); the radius is the shorter (center to edge).
A pizza has a radius of 7 inches. What is its diameter?
d = 2 x 7 = 14 inches.
A bicycle wheel has a diameter of 26 inches. What is its radius?
r = 26 / 2 = 13 inches.
A circular garden path goes straight through the center and is 12 meters long. What is the radius?
The path through the center is the diameter: d = 12. Radius = 12 / 2 = 6 meters.
What is the most common radius/diameter error?
Confusing radius with diameter and using the wrong value in calculations. Remember: diameter is the bigger word and the bigger number. When you have the radius and need the diameter, multiply by 2. When you have diameter and need radius, divide by 2.