Area and Perimeter • Topic 5 of 6

Circles

A circle’s area is πr² and its circumference (the “perimeter” of a circle) is 2πr, where r is the radius. The SAT usually wants answers in terms of π, such as 25π, rather than as decimals. If you are given the diameter, halve it to get the radius before using either formula. Keep the two formulas straight: area uses r² (square units), while circumference uses 2r (a length). Mixing them — using 2πr when area is wanted, or πr² for the distance around — is the most common error. You can also reverse them to find the radius from a given area or circumference.

A circle with radius 5Circler=5Area = πr² = 25π    Circumference = 2πr = 10π

✅ Solved examples

1. A circle has radius 5. Find its area in terms of π.
πr² = 25π.
2. A circle has radius 5. Find its circumference.
2πr = 10π.
3. A circle has radius 8. Find its area.
π(8)² = 64π.
4. A circle has diameter 12. Find its area.
r = 6, so π(6)² = 36π.

✏️ Practice — try these, take hints as needed

1. A circle has radius 3. Find its area in terms of π.
πr².
π(3)².
—
9π.
2. A circle has radius 7. Find its circumference.
2πr.
2π(7).
—
14π.
3. A circle has radius 10. Find its area.
π(10)².
—
—
100π.
4. A circle has diameter 8. Find its area.
r = 4.
π(4)².
—
16π.
5. A circle has radius 6. Find its circumference.
2π(6).
—
—
12π.

📝 Topic test — 8 questions

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