Diameter and Radius
The diameter of a circle is the distance across the circle through its center, and the radius is the distance from the center to the edge. In Grade 6 Saxon Math Course 1 (Chapter 3: Number, Operations, and Geometry), students learn the fundamental relationship: the diameter equals twice the radius (d = 2r) and the radius equals half the diameter (r = d/2). For a circle with radius 7 cm, the diameter is 14 cm. Every formula for circumference and area uses either r or d, making the ability to convert between them essential. All radii of a circle are equal.
Key Concepts
Property The diameter is the distance across a circle through its center. The radius is the distance from the center to the circle. For any circle, the diameter is twice the length of the radius ($d = 2r$).
Examples If a circle's radius is 4 cm, its diameter is $2 \times 4 \text{ cm} = 8 \text{ cm}$. A pizza has a diameter of 16 inches. Its radius, from the center to the crust, is $\frac{16 \text{ in}}{2} = 8 \text{ inches}$. If the diameter of a Ferris wheel is 50 meters, its radius is half of that, which is 25 meters.
Explanation Think of the radius as a single spoke on a bicycle wheel, stretching from the center hub to the outer rim. The diameter is like a special spoke that goes all the way across the wheel, passing through the center. That's why the diameter is always double the radius—it’s made of two radii lined up back to back!
Common Questions
What is the relationship between diameter and radius?
The diameter equals twice the radius: d = 2r. The radius equals half the diameter: r = d/2.
A circle has radius 9 cm. What is its diameter?
d = 2 x 9 = 18 cm.
A circle has diameter 26 mm. What is its radius?
r = 26 / 2 = 13 mm.
What is the difference between diameter and radius?
The radius goes from the center to the edge (half the distance across). The diameter goes all the way across the circle through the center.
Why must you know the difference between radius and diameter?
The circumference formula C = 2 x pi x r uses radius, while C = pi x d uses diameter. The area formula A = pi x r squared uses radius only. Using the wrong value gives an incorrect answer.