Study guides › Level 7 · Geometry

Arc length and pizza slices (sectors)

Level 7 · Geometry · for questions like “A pizza has a radius of 6 inches. A slice has a 60° angle. What is its area?”

💡 The idea

An arc or a slice is just a fraction of the whole circle, and that fraction is angle ÷ 360°.

• arc length = (angle ÷ 360) × 2πr
• slice area = (angle ÷ 360) × πr²

🪜 The steps

1. Work out the fraction: angle ÷ 360 (60° is 1/6).
2. Work out the whole: the circumference 2πr, or the area πr².
3. Multiply.

✏️ Worked examples

1. Radius 6, 60° slice, area? The whole is 36π, and 1/6 of it is 6π square inches.

2. Radius 9, 120° arc, length? The whole is 18π, and 1/3 of it is 6π.

⚠️ Watch out

• Area uses r², length uses 2r.
• Leave π in the answer unless the question asks for a decimal.

🎯 Try these

1. Radius 4, 90° slice: area?
2. Radius 10, 72° arc: length?
3. Radius 12, 30° slice: area?

Answers: 1) 4π 2) 4π 3) 12π

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.