Quick Notes

Quick Notes

Mathematics Chapter 5: Circles
5.3 Circumference and Area of a Circle
 
5.3  Circumference and Area of a Circle
 
  Definition  
     
 

The circumference of a circle is the measurement around a circle.

  
 
Relationship between circumference and diameter:
 
(i)  

\(\dfrac{\text{Circumference}}{\text{Diameter}}= \pi\),

where \(\pi = 3.142\) or \(\pi=\dfrac{22}{7}\)
     
(ii)   \(\begin{aligned} \text{Circumference} &= \pi \times \text{diameter} \\&=\pi d\end{aligned}\)
     
(iii)   \(\begin{aligned} \text{Circumference} &= \pi \times 2 \times \text{radius}\\&=2\pi r \end{aligned}\)
 
Area of a Circle:
 
\(\text{Area of circle} = \pi r^2\)
 
Length of Arc in a Circle:
 
\(\begin{aligned}\dfrac{\text{Length of arc}}{\text{Circumference}} &= \dfrac{\text{Angle at centre}}{360 ^{\circ}} \\\\\dfrac{\text{Length of arc}}{2\pi r}&=\dfrac{\theta}{360 ^{\circ}} \end{aligned}\)
 
Area of a Sector:
 
\(\begin{aligned}\dfrac{\text{Area of sector}}{\text{Area of circle}} &= \dfrac{\text{Angle at centre}}{360 ^{\circ}}\\\\\dfrac{\text{Area of sector}}{\pi r^2} &= \dfrac{\theta}{360 ^{\circ}}\end{aligned}\)