Area and Circumference — SAT Math Explained
Circumference is the distance around a circle (its perimeter). Area is the amount of space enclosed inside the circle.
The Core Idea
Both formulas use π (pi ≈ 3.14159), the universal constant relating a circle's circumference to its diameter. Pi is irrational — it never terminates or repeats — but is approximately 3.14 for most calculations.
Step-by-Step: How to Approach Area and Circumference
Identify whether you have radius or diameter (convert if needed: r = d/2)
Choose the correct formula
Substitute the value
Calculate — either leave in terms of π or compute decimal approximation
Formulas
C = 2πr or C = πd
A = πr²
Pi Explained
π = C/d for any circle — the ratio of circumference to diameter is always the same constant, regardless of circle size. This is one of the most remarkable facts in mathematics.
Exact Vs Approximate
Leave answer in terms of π: '6π cm'
Substitute π ≈ 3.14 or use calculator value
Inverse Problems
If given circumference or area, work backwards to find radius: C = 2πr → r = C/(2π); A = πr² → r = √(A/π)
Common Errors to Avoid
Squaring the diameter instead of the radius in area (most common error)
Using diameter in A = πr² without first converting to radius
Confusing circumference formula with area formula
Practice: Area and Circumference
5 SAT-style questions. Select your answer and get an instant explanation.
Circle radius 7. Circumference C = 2πr equals:
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