ACT · Coordinate Geometry · Circles in the coordinate plane
Question act-q-00430
Medium Multiple choice No calculator
The question
A circle has radius 10. What is its area, in terms of π?
- 20π
- 100π
- 10π
- 200π
Show answer & worked solution
Answer: 100π
Worked solution. Area of a circle is πr². Here r = 10, so area = π × 10² = 100π.
Why each wrong choice is wrong. Confusing area (πr²) with circumference (2πr) is the dominant error here. The 2πr distractor catches it perfectly.
Test-day tactic. Area scales as the square of the radius; circumference scales linearly. When in doubt, sketch a unit circle and check.
About this question type
Items test the standard form (x − h)² + (y − k)² = r² and conversions to and from general form by completing the square.
You will see a question shaped like this one on roughly every other official ACT form, typically at a moderate position in the section — solidly within the range that separates a 600-band student from a 700-band student. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.