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 calculate what fraction of a full turn the angle is.
Example
Calculate the area of this sector which has a 60° angle to one decimal place.
60° is 1/6 of a full turn (360°).
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: \(\text{Sector area} = \pi \times r^2 \times \frac{\text{angle}}{360}\)
Question
Calculate the minor sector area to one decimal place.
Sector area = \(\pi \times 3.5^2 \times \frac{144}{360} = 15.4~\text{cm}^2\)
Question
Calculate the major sector area to one decimal place.
The major sector has an angle of \(360 - 110 = 250^\circ\).
Sector area = \(\pi \times 6^2 \times \frac{250}{360} = 78.5~\text{cm}^2\)