Circle
Parts of A Circle
Area of A Circle
\(A = \pi\times r^2\)
\(\pi = \dfrac{22}{7} = 3.14\)
\(A =\dfrac{1}{4} \pi\times d^2\)
\(\pi = \dfrac{22}{7} = 3.14\)
Area of A Sector
\(\text{Area of sector} = \dfrac{1}{2}\times r^2 \times \theta\)
\(\theta\) in radian
\(\text{Area of sector} = \dfrac{\theta}{360^\circ}\times \pi\times r^2\)
\(\theta\) in degree
Circumference of A Circle
\(\text{circumference of circle} = 2\times \pi\times r\)
\(\pi = \frac{22}{7} = 3.14\)
\(r = \text{radius}\)
\(\text{circumference of circle} =\pi\times d\)
\(d = \text{diameter}\)
Arc Length
\(\text{If θ is measured in degrees then:}\)
\(\text{Arc length} = \frac{\theta}{360^\circ} \times \text{circumference of circle} \)
\(\text{Arc length} = \frac{\theta}{360^\circ} \times 2\times \pi \times r \)
\(\text{If θ is measured in radians then:}\)
\(\text{Arc length} = \theta \times r\)
\(1 \pi \text { radians} = 180^\circ\)
\(1 \text{ radians ≈ 57.3°}\)
Exercise