How it works
For a circle with radius r and diameter d = 2r:
Area = πr² · Circumference = 2πr = πd
"In terms of π" means you leave π as a symbol: a circle of radius 6 has area 36π, not 113.1. The most common slip is using the diameter where the formula needs the radius, so write down r before anything else.
Finding the radius
A circle inscribed in a square touches all four sides, so its diameter equals the side of the square. A circle that passes through all four corners of a rectangle has the rectangle's diagonal as its diameter. A ring (annulus) between two circles has area π(R² − r²).
Circle Area practice problems with solutions
These problems come from Mathyessy's question bank. Try each one before opening the solution.
A circle has radius 6. Give the area in terms of π — enter the number before π.
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Answer: 36π
Area = π × 6² = 36π.
A circle has area 49π. Find its radius.
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Answer: 7
πr² = 49π, so r² = 49 and r = 7.
A ring has outer radius 9 and inner radius 7. Give the ring area in terms of π — enter the number before π.
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Answer: 32π
Subtract the inner circle from the outer one: 81π − 49π = 32π.
A rectangle measures 12 by 16. Its diagonal is the diameter of a circle. Give the circle area in terms of π — enter the number before π.
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Answer: 100π
The diagonal is √(12² + 16²) = √400 = 20, so the radius is 10 and the area is 100π.
Keep going
Related topics
- Arc length and sector area
- Pythagorean theorem
- Surface area
- Special right triangles: 45-45-90 and 30-60-90
Related practice sets in the app
All Geometry topics · Contest math practice by topic · MATHCOUNTS practice · AMC 8 practice