Measurement - Circumference and Area of Circles

The Radius ($r$) is a straight line segment from the center of the circle to any point on its boundary. The Diameter ($d$) is a straight line passing through the center to connect two points on opposite sides of the boundary. Visually, the diameter is exactly twice the length of the radius, expressed as $d = 2r$.

Circumference is the total distance around the edge of the circle, functioning exactly like the perimeter of a polygon. If you were to 'unroll' the circle's boundary into a straight line, the length of that line would be the circumference.

The constant $\pi$ (Pi) is an irrational number approximately equal to $3.14$ or $\frac{22}{7}$. It represents the fixed ratio between a circle's circumference and its diameter ($C \div d = \pi$). Regardless of the circle's size, this ratio remains constant.

The Area of a circle is the total surface space enclosed within its boundary. While circumference measures length in linear units (like $cm$), area measures the 'flat' space inside in square units (like $cm^2$).

To visualize the Area formula ($A = \pi r^2$), imagine a square with side length equal to the radius ($r$). The area of this 'radius square' is $r^2$. The circle's total area is slightly more than $3$ (specifically $\pi$) of these squares.

A Semicircle is exactly half of a circle, created by cutting the circle along its diameter. Its curved boundary is half of the total circumference, but its total perimeter must also include the straight diameter line.

A Quadrant is one-fourth of a circle. Its area is calculated as $\frac{1}{4} \pi r^2$. Visually, it looks like a slice of pie with two straight edges (radii) meeting at a $90^{\circ}$ angle at the center.