Circles
Grades 6–8 Geometry Circles π
A circle is every point exactly one radius from a center. The diameter crosses through: d = 2r. The circumference is the trip around the outside.
π — the shape of every circle
Divide any circle's circumference by its diameter — coffee cup or planet — you always get π ≈ 3.14159…
Circumference C = πd = 2πr
Area A = πr²
- r = 5 → C = 10π ≈ 31.4
- r = 5 → A = 25π ≈ 78.5
Watch out
Circumference uses the diameter (or 2r), area uses the radius
squared. Mixing them up is the classic circle error —
C is a length, A is an area, so the units must differ too.
Estimating
π ≈ 3 does the mental math. r = 4 → A ≈ 48 (real: 50.3). Close
enough to sanity-check any answer instantly.
Practice
A circle with r = 6 has diameter ___
r = 10 → circumference ≈ ___ (use π ≈ 3.14)
r = 3 → area ≈ ___ (use π ≈ 3.14)
π is the ratio of:
Next: perimeter & area · Back: quadrilaterals