Area of a Shaded Region

Learn how to calculate the area between two concentric circles.

Understanding Concentric Circles

Concentric circles are two or more circles that share the same center point. The region between two concentric circles is called an annulus.

To find the area of the shaded region (the annulus), you need to subtract the area of the smaller, inner circle from the area of the larger, outer circle.

R is the radius of the larger circle.
r is the radius of the smaller circle.

The Formula

Step 1: Area of a Single Circle

The formula to find the area of any circle is π (pi) times the radius squared.

Area = πr²

Step 2: Area of the Shaded Region

Subtract the area of the small circle from the area of the large circle.

Shaded Area = (Area of Large Circle) - (Area of Small Circle)

Shaded Area = (πR²) - (πr²)

Shaded Area = π(R² - r²)

Example Calculation

Let's walk through an example. Assume π ≈ 3.14.

Given:

Radius of the large circle (R) = 10 cm
Radius of the small circle (r) = 6 cm

1. Calculate the area of the large circle:

Area_large = πR² = 3.14 × (10)² = 3.14 × 100 = 314 cm²

2. Calculate the area of the small circle:

Area_small = πr² = 3.14 × (6)² = 3.14 × 36 = 113.04 cm²

3. Subtract the small area from the large area:

Shaded Area = 314 - 113.04 = 200.96 cm²

Final Answer

The area of the shaded region is 200.96 cm².