Математика22 мин

Circles

Circumference, area, sector and arc length, plus the must-know circle theorems.

Core formulas

C = 2\pi r,\quad A = \pi r^2

\text{Arc length} = r\theta,\quad \text{Sector area} = \tfrac{1}{2}r^2\theta

\theta

in radians.

\text{Arc} = \dfrac{\theta°}{360°} \cdot 2\pi r,\quad \text{Sector} = \dfrac{\theta°}{360°} \cdot \pi r^2

Same in degrees.

Жаттығу

A sector has radius 10 cm and angle 36°. Arc length?

Жауап пен түсініктемені көру

Жауап: $2\pi$ cm $\approx 6.28$ cm

Arc = $(36/360) \cdot 2\pi \cdot 10 = 2\pi$ cm.