Area of a Circle Examples in Math
Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Area of a Circle.
This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.
Concept Recap
The amount of space enclosed inside a circle, calculated as \pi times the square of the radius.
Imagine cutting a pizza into many thin slices and rearranging them into a shape that looks like a rectangle. The 'height' of that rectangle is the radius r, and the 'width' is half the circumference (\pi r). So the area is r \times \pi r = \pi r^2.
Read the full concept explanation →How to Use These Examples
- Read the first worked example with the solution open so the structure is clear.
- Try the practice problems before revealing each solution.
- Use the related concepts and background knowledge badges if you feel stuck.
What to Focus On
Core idea: The area of a circle grows with the square of the radius—double the radius, quadruple the area.
Common stuck point: The formula uses the radius, not the diameter. If given the diameter, divide by 2 first.
Worked Examples
Example 1
easySolution
- 1 The area enclosed by a circle of radius r is A = \pi r^2. This can be understood by imagining the circle divided into many thin triangles from the centre; their combined area gives \frac{1}{2} \times (2\pi r) \times r = \pi r^2.
- 2 Substitute r = 6 cm: A = \pi(6)^2 = \pi \times 36.
- 3 Result: A = 36\pi cm² \approx 113.1 cm². Note that doubling the radius quadruples the area (since r is squared), a key scaling insight.
Answer
Example 2
mediumPractice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
hardExample 2
mediumBackground Knowledge
These ideas may be useful before you work through the harder examples.