Sector area
Two The distance from the centre of a circle to its circumference. The plural of radius is radii. separate the area of a circle into two sectors - the major sector and the minor sector.
To calculate the sector area, first find what fraction of the whole circle we have.
Example
Calculate the area of this sector which has a 60掳 angle to one decimal place.
60掳 is one sixth of a full turn (360掳).
The sector is \(\frac{1}{6}\) of the full area.
Remember the area of a circle = \(\pi r^2\)
The sector area is: \(\frac{1}{6} \times \pi \times 4^2 = 8.4~\text{cm}^2\)
The formula to calculate the sector area is: \(\text{Sector area} = \frac{\text{angle}}{360} \times \pi \times r^2 \)
Question
Calculate the minor sector area to one decimal place.
Sector area = \(\frac{144}{360} \times \pi \times 3.5^2 = 15.4~\text{cm}^2\)
Question
Calculate the major sector area to one decimal place.
The major sector has an angle of \(360 - 110 = 250^\circ\).
Sector area = \(\frac{250}{360} \times \pi \times 6^2 = 78.5~\text{cm}^2\)