Area and Circumference of a Circle

$A = \pi \times 5^2 = 25\pi \approx 78.54 \text{ cm}^2$

$C = 2\pi \times 5 = 10\pi \approx 31.42 \text{ cm}$

A small pizza has diameter 24 cm ($r = 12$ cm) and a large has diameter 30 cm ($r = 15$ cm).

Small: $A = \pi \times 12^2 = 144\pi \approx 452 \text{ cm}^2$

Large: $A = \pi \times 15^2 = 225\pi \approx 707 \text{ cm}^2$

The large pizza is about 57 % bigger than the small — despite looking only 25 % wider. Knowing circle areas helps you judge value for money.

A rotating sprinkler reaches 5 m in every direction.

$A = \pi \times 5^2 = 25\pi \approx 78.5 \text{ m}^2$

A gardener uses this to decide how many sprinklers cover a 20 m × 10 m lawn (200 m²): at least 3 sprinklers with some overlap.

An architect designs a circular window with diameter 0.8 m ($r = 0.4$ m).

$A = \pi \times 0.4^2 = 0.16\pi \approx 0.50 \text{ m}^2$

Glass is sold by the square metre. This tells the glazier exactly how much material to order and quote.