Area of a Circle Math Example 1

Solution

1. 1
   The area enclosed by a circle of radius $r$ is $A = \pi r^2$. This can be understood by imagining the circle divided into many thin triangles from the centre; their combined area gives $\frac{1}{2} \times (2\pi r) \times r = \pi r^2$.
2. 2
   Substitute $r = 6$ cm: $A = \pi(6)^2 = \pi \times 36$.
3. 3
   Result: $A = 36\pi$ cm² $\approx 113.1$ cm². Note that doubling the radius quadruples the area (since $r$ is squared), a key scaling insight.