Sector Area Practice Problems

Formulas you need

• Sector area (degrees): $A = \dfrac{\theta}{360}\cdot \pi r^2$
• Sector area (radians): $A = \tfrac{1}{2} r^2 \theta$
• Arc length: $L = \dfrac{\theta}{360}\cdot 2\pi r$

where r = radius, θ = central angle (degrees), A = sector area

Generate a new problem

Pick a difficulty, work it out, then check your answer. Every press gives a new question — the numbers are drawn fresh each time, so you can keep going.

Warm-up

1. A circle of radius r = 4 has a central angle of 30°. Find the sector area (A).

   Answer & working

   4.19 units²

   A = (θ/360) · πr² = (30/360) · π · 4² ≈ 4.19

2. A circle of radius r = 2 has a central angle of 135°. Find the arc length (L).

   Answer & working

   4.71 units

   arc L = (θ/360) · 2πr ≈ 4.71

3. A circle of radius r = 4 has a central angle of 180°. Find the sector area (A).

   Answer & working

   25.13 units²

   A = (θ/360) · πr² = (180/360) · π · 4² ≈ 25.13

4. A circle of radius r = 3 has a central angle of 60°. Find the arc length (L).

   Answer & working

   3.14 units

   arc L = (θ/360) · 2πr ≈ 3.14

5. A circle of radius r = 1 has a central angle of 30°. Find the sector area (A).

   Answer & working

   0.26 units²

   A = (θ/360) · πr² = (30/360) · π · 1² ≈ 0.26

Core practice

1. A circle of radius r = 9 has a central angle of 240°. Find the sector area (A).

   Answer & working

   169.65 units²

   A = (θ/360) · πr² = (240/360) · π · 9² ≈ 169.65

2. A circle of radius r = 2 has a central angle of 120°. Find the arc length (L).

   Answer & working

   4.19 units

   arc L = (θ/360) · 2πr ≈ 4.19

3. A circle of radius r = 1 has a central angle of 90°. Find the sector area (A).

   Answer & working

   0.79 units²

   A = (θ/360) · πr² = (90/360) · π · 1² ≈ 0.79

4. A circle of radius r = 10 has a central angle of 180°. Find the arc length (L).

   Answer & working

   31.42 units

   arc L = (θ/360) · 2πr ≈ 31.42

5. A circle of radius r = 3 has a central angle of 210°. Find the sector area (A).

   Answer & working

   16.49 units²

   A = (θ/360) · πr² = (210/360) · π · 3² ≈ 16.49

Stretch

1. A circle of radius r = 1.5 has a central angle of 135°. Find the sector area (A).

   Answer & working

   2.65 units²

   A = (θ/360) · πr² = (135/360) · π · 1.5² ≈ 2.65

2. A circle of radius r = 9.5 has a central angle of 210°. Find the arc length (L).

   Answer & working

   34.82 units

   arc L = (θ/360) · 2πr ≈ 34.82

3. A circle of radius r = 7.5 has a central angle of 240°. Find the sector area (A).

   Answer & working

   117.81 units²

   A = (θ/360) · πr² = (240/360) · π · 7.5² ≈ 117.81

4. A circle of radius r = 1.5 has a central angle of 270°. Find the arc length (L).

   Answer & working

   7.07 units

   arc L = (θ/360) · 2πr ≈ 7.07

5. A circle of radius r = 8.5 has a central angle of 60°. Find the sector area (A).

   Answer & working

   37.83 units²

   A = (θ/360) · πr² = (60/360) · π · 8.5² ≈ 37.83