Circumference and Area of a Circle
C = 2πr and A = πr².
About this topic
The circumference, the distance around a circle, is C = 2πr = πd, and the area is A = πr². The constant π ≈ 3.14159 is the ratio of any circle's circumference to its diameter, and it is irrational.
Because area depends on the radius squared, doubling the radius quadruples the area. Cutting a circle into thin sectors and rearranging them into a near-rectangle explains the area formula. Wheels, pipes, pizzas and lenses all rely on these formulas.
Worked example: a pizza has diameter 30 cm, so r = 15. Its circumference is 2π(15) ≈ 94.2 cm and its area is π(225) ≈ 706.9 square cm. A 40 cm pizza has r = 20 and area about 1256.6, nearly 1.8 times larger even though the diameter rose by only a third, so the bigger pizza is a better deal than it looks. A bicycle wheel with a 0.7 m diameter travels about 2.2 m each turn.
Engineers use these formulas for pipes, tanks and gears. The most common error is using the diameter in place of the radius in A = πr², which makes the answer four times too big. Another is mixing up C and A: circumference is a length, area is square units. Use 3.14 or the π button as the problem asks, and leave answers in terms of π when asked for an exact value, such as 225π.
Key ideas
- π ≈ 3.14159
- Area grows with the square of the radius
- Doubling r quadruples area
Quick check
Use cases: where Circumference and Area of a Circle helps
- Homework: review the key idea behind Circumference and Area of a Circle before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Circumference and Area of a Circle without notes.
- Visual learning: play with the interactive lab to see how Circumference and Area of a Circle changes when you adjust its inputs.
- Teaching a friend: explain Circumference and Area of a Circle in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Circumference and Area of a Circle?
C = 2πr and A = πr².
What will I learn in Circumference and Area of a Circle?
π ≈ 3.14159. Area grows with the square of the radius. Doubling r quadruples area.
Is Circumference and Area of a Circle part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Circumference and Area of a Circle lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Circumference and Area of a Circle?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
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