Circle: Area, Circumference, Arc

A = π r^{2}, C = 2 π r, s = r θ (θ rad)

Sector area on p. 42 is A = φ r²/2 with φ = s/r in radians (also A = s r / 2). A full circle is that formula at φ = 2π, which gives A = π r² and circumference C = 2π r. Those full-circle formulas are the substitution, not separate boxed lines.

$r$ (m): Radius
$A$ (m²): Area
$C$ (m): Circumference
$s$ (m): Arc length
$θ$: Central angle (radians)

Step-by-step solved example

r = 3 m. Find A, C, and the arc for θ = 2 rad.

Radius, arc, and sector — the circular analog of the triangle figure.

1. Area and circumference
A = 9π ≈ 28.27 m². C = 6π ≈ 18.85 m.
$A = 9 π, C = 6 π$
2. Arc
s = rθ = 3×2 = 6 m.
$s = 6 m$

Answer: A = 9π m², C = 6π m, s = 6 m

10 practice questions

0/10 correct

1.r = 3. Area A equals

2.r = 5. Circumference C equals

3.Diameter equals

4.θ = π/2 rad, r = 4. Arc s equals

5.A full circle in radians is

6.Sector area equals

7.Doubling r multiplies area by

8.C / D equals

9.θ = 2 rad, r = 6. s equals

10.r = 10. Area A equals