Circles: Circumference and Area

Parts of a Circle

• Center: The middle point
• Radius ($r$): Distance from center to edge
• Diameter ($d$): Distance across the circle through the center ($d = 2r$)

Pi ($\pi$)

$\pi \approx 3.14159...$

Pi is the ratio of any circle's circumference to its diameter. It's an irrational number (never ends, never repeats).

Circumference (Perimeter of a Circle)

$C = \pi d = 2\pi r$

Example: Circle with radius 5 cm: $C = 2\pi(5) = 10\pi \approx 31.42 \text{ cm}$

Area of a Circle

$A = \pi r^2$

Example: Circle with radius 5 cm: $A = \pi(5)^2 = 25\pi \approx 78.54 \text{ cm}^2$

Finding Radius from Circumference

If $C = 18.84$ cm: $r = \frac{C}{2\pi} = \frac{18.84}{2(3.14)} = 3 \text{ cm}$

Semicircle

A semicircle is half a circle:

• Area: $A = \frac{1}{2}\pi r^2$
• Perimeter: $P = \pi r + 2r$ (curved part + diameter)

Word Problems

A circular pool has a diameter of 24 feet. How much fencing is needed around it? $C = \pi d = \pi(24) = 24\pi \approx 75.4 \text{ feet}$

Remember: Use radius in both formulas. If given diameter, divide by 2 first!