Pre-Algebra
Geometry
Circles: area and circumference
20 practice questions
0 video lessons
Theory + worked examples
Circles: Area and Circumference
Texas Pre-Algebra (TEKS) • Standard 7.9(B) • Geometry
Circles: Area and Circumference is a topic in Geometry in the Texas Essential Knowledge and Skills. It is aligned to Standard 7.9(B), which requires students to find the area and circumference of circles.
A circle's circumference is \(2\pi r\) and its area is \(\pi r^2\).
Theory
For a circle with radius \(r\) (and diameter \(d=2r\)):
- Circumference: \(C=2\pi r=\pi d\).
- Area: \(A=\pi r^2\).
\(\pi\approx3.14\) is the ratio of circumference to diameter.
The radius of a circle.
Circle formulas.
Circle measures:
\[C=2\pi r,\qquad A=\pi r^2\]
Circumference is a length; area is squared units.
How to use circle formulas
- Find the radius (half the diameter).
- For circumference, use \(2\pi r\).
- For area, use \(\pi r^2\).
- Substitute \(\pi\approx3.14\) if needed.
Example 1 — Circumference
Find the circumference of a circle with \(r=5\). (Use \(\pi\approx3.14\).)
Solution
\(C=2\pi r\).
| \(2(3.14)(5)\) | \(=\) | \(31.4\) |
Example 2 — Area
Find the area with \(r=5\).
Solution
\(A=\pi r^2\).
| \(3.14\cdot25\) | \(=\) | \(78.5\) |
Example 3 — From diameter
A circle has diameter \(10\). Find the radius.
Solution
Half the diameter.
| \(r\) | \(=\) | \(5\) |
Example 4 — Circumference from d
Find \(C\) for diameter \(8\).
Solution
\(C=\pi d\).
| \(3.14\cdot8\) | \(=\) | \(25.12\) |
Common pitfalls
Area uses \(r^2\); circumference uses \(r\).
The radius is half the diameter.
Don't square the \(\pi\).
Frequently asked questions
What is the circumference formula?
\(C=2\pi r\).
What is the area formula?
\(A=\pi r^2\).
What is the radius?
Half the diameter.
Area with \(r=5\)?
About \(78.5\).
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