Circumference and Area of Circles
Overview
Circumference is the distance around a circle and area is the space inside it, and both come straight from the radius: C = 2πr (or C = πd) and A = πr². Portions of the circle follow the same proportion — an arc is a fraction of the circumference, and a sector is that same fraction of the area, with the fraction set by the central angle over 360°. Following the convention in the notes, answers use 3.14 for π unless a problem asks for an exact answer, which keeps π in the result.
Vocabulary
- Circumference
- The distance around a circle. C = 2πr, or equivalently C = πd.
- Area of a Circle
- The measure of the region enclosed by a circle: A = πr², reported in square units.
- Exact Answer
- An answer that keeps the symbol π instead of substituting a decimal approximation. When a problem says "exact," no rounding is allowed.
- Arc Length
- The distance along an arc, equal to the fraction (arc measure ÷ 360°) of the circle's circumference.
- Sector
- A region bounded by two radii of a circle and the arc between them. Its area is the fraction (central angle ÷ 360°) of the circle's area.
Main Ideas
- Start every problem by identifying the radius. If you are given the diameter, halve it first — using the diameter where the radius belongs is the most common error in this lesson.
- Circumference is a length (units), and area is measured in square units.
- Use 3.14 for π unless the problem asks for an exact answer; an exact answer leaves π in the result.
- Arc length and sector area are both found with the proportion (central angle) / 360 = (part) / (whole).
Lesson Notes
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Lesson Video
This lesson has 2 videos. Watch them in order.
Circumference and Area - part 1
Circumference and Area - part 2
Practice Problems
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Download the practice worksheet for this lesson, work the problems, then check your work with the solutions.