Circle measures
Compare circumferences, areas, arcs and sectors. Change the radius or angle to test your reasoning.
Radius and scale
1 comparison · No time limit · Explore after checking
Example
Example
Compare how area and circumference scale.
Review the comparison
Circle B has 3 times the radius of circle A.
Both radii are positive.
Both circles use the same drawing scale.
Area of B ÷ area of A
Circumference of B ÷ circumference of A
Choose an answer to try the example.
Why?
Explore the relationship
Make circle A's area 16π square units.
In this drawing
Need a clue?
Solve πr² = 16π using a positive radius.
Example positions
Resize both circles while keeping their radius ratio fixed.
The controls preserve the givens. Examples illustrate the rule; the explanation proves it.
Go further Apply the idea
Further practice does not change your comparison score.
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Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is usedHelp
Choose whether Quantity A is greater, Quantity B is greater, the quantities are equal, or the relationship cannot be determined. Use only the stated givens. A drawing shows one possible case.
Your first checked answer counts. A shown answer counts as 0 correct. A checked comparison is saved immediately, so you can explore afterward without losing your result. An unfinished comparison is not saved as a result.
After checking, use the controls to solve an exploration goal. When the relationship cannot be determined, save two valid cases with different comparisons. Open Go further to apply the idea to a new question. These activities are optional and do not change your score.
Angles and trigonometric functions use degrees. Levels increase the mathematical complexity; they do not measure IQ.
About this practice
Learn a method
Measure a circle sectorCompare circumferences, areas, arcs and sectors. Change the radius or angle to test your reasoning.
For a broader mix of practices, explore the geometry practice test. Membership is required to start a test.
Report a problem
Optional and off by default. Share starts, completions, replays and error categories. For visits from ChatGPT, starts and completions can also include the first QuickenBrain page and broad country. No answers, drawings or names.
How this data is used