SAT Math: Area and Circumference of a Circle
38+ practice questions in Praczo
The concept, explained
- 1
Area: A = πr². Circumference: C = 2πr = πd. These are on the SAT reference sheet, but use them fluently.
- 2
Radius is half the diameter. Always confirm which one you are given before substituting.
- 3
Sector (pizza slice): sector area = (θ/360°) × πr² and arc length = (θ/360°) × 2πr, where θ is the central angle in degrees.
- 4
Working backward: given circumference C = 2πr → r = C/(2π). Given area A = πr² → r = √(A/π).
- 5
Key radian conversions: 360° = 2π rad. 180° = π. 90° = π/2. 45° = π/4.
- ✗ Using diameter instead of radius: a circle with diameter 10 has r = 5, so A = π(5)² = 25π — not π(10)² = 100π.
- ✗ Forgetting to square r: A = πr², not πr. If r = 6, area = 36π.
SAT-style practice
A circle has a circumference of 10π. What is the area of the circle?
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