Lesson 27: Measures of a Circle

New Concept

This lesson defines a circle's key parts. The diameter is the distance across a circle, the radius is from the center to the edge, and circumference is the distance around.

For any circle, the diameter is twice the length of the radius.

What’s next

Next, you'll practice identifying these measures and use the relationship between the radius and diameter to solve problems.

Property

The circumference is the distance around the circle. This distance is the same as the perimeter of a circle.

Examples

• The length of the fence needed to enclose a circular garden is its circumference.
• If you trace the edge of a dinner plate, the distance your finger travels is the plate's circumference.
• The total length of a circular racetrack is measured by its circumference.

Explanation

Imagine you're walking along the edge of a giant, perfectly round pizza. The total distance you travel to get back to where you started is the circumference! It’s just a fancy name for a circle's perimeter. So, when someone mentions the distance around a circular pool or a running track, you'll know they mean its circumference.

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!