Area of a Circle

🎯 What Will We Learn Today?

How much space does a circle take up? Today we'll learn how to calculate the area of a circle — the space inside the curved edge.

📚 What Is Area?

Area tells us how much flat space a shape covers. For a circle, the area is the amount of space inside the circular boundary. We measure area in square units (like square centimeters or square inches).

📐 The Formula

The formula for the area of a circle is:

A = π × r²

Where:

A = area

π ≈ 3.14

r = radius of the circle

r² = radius × radius

🔍 Where Does the Formula Come From?

Imagine cutting a circle into many thin slices (like pizza slices) and rearranging them. They form a shape that looks almost like a rectangle! The width is about π × r (half the circumference) and the height is r (the radius). So:

Area ≈ (π × r) × r = π × r²

Cool, right? Math is everywhere — even in pizza!

🎮 Let's Calculate!

Example 1: A pizza has a radius of 8 inches. What is its area?

A = π × 8² = 3.14 × 64 = 200.96 square inches

Example 2: A circular garden has a diameter of 10 meters. What is its area?

First find radius: r = 10 ÷ 2 = 5 m

A = π × 5² = 3.14 × 25 = 78.5 square meters

Example 3: Which has more area — a circle with radius 4 or a square with side 7?

Circle area: 3.14 × 16 = 50.24

Square area: 7 × 7 = 49

The circle has slightly more area!

💡 Quick Tips

Always use the radius (not diameter) in A = πr²

If you know the diameter, divide by 2 to get the radius

Area is always in square units

📝 Practice Problems

Find the area of a circle with radius 3 cm. (Use π ≈ 3.14)

A circle has diameter 12 in. What is its area?

If the area of a circle is 78.5 sq cm, what is the radius? (Hint: work backwards!)

Compare: circle radius 5 vs square side 9 — which has more area?

🎮 Play a Game!

Practice with circles and fractions in Dirt Bike Fractions!