Study guides › Level 6 · Master

Circles: area and the distance around

Level 6 · Master · for questions like “A circle has a radius of 6 cm. What is its area?”

💡 The idea

• Area = π × r² (r is the radius).
• Circumference (the distance around) = 2 × π × r = π × diameter.

Leaving π in the answer (like 36π) keeps it exact.

🪜 The steps

1. Make sure you have the radius. If you're given the diameter, halve it.
2. For area: square the radius, then write π after it.
3. For the distance around: double the radius, then write π after it.
4. Going backwards from the area: divide by π, then take the square root.

✏️ Worked examples

1. Radius 6. Area? 6² = 36, so 36π sq cm.

2. Radius 6. Distance around? 2 × 6 = 12, so 12π cm.

3. The area is 49π. Radius? 49 = 7², so 7 cm.

⚠️ Watch out

• Area uses r², not 2r. With radius 6: the area is 36π, but the distance around is 12π.
• Diameter or radius? Read carefully.

🎯 Try these

1. Radius 5. Area?
2. Radius 9. Distance around?
3. The area is 100π. Radius?

Answers: 1) 25π 2) 18π 3) 10

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