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.
The formula to calculate the sector area is: \(\text{Sector area} = \frac{\text{angle}}{360} \times \pi r^2 \)
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: \(\frac{1}{6} \times \pi \times 4^2 = 8.4~\text{cm}^2\)
Question
Calculate the sector area to 1 decimal place.
Area of sector = \(\frac{144^\circ}{360^\circ} \times \pi \times 3.5^2 = 15.4~\text{cm}^2\)
Question
Calculate this major sector area to 1 decimal place.
The major sector has an angle of \(360^\circ - 110^\circ = 250^\circ\).
Area of sector = \(\frac{250^\circ}{360^\circ} \times \pi \times 6^2 = 78.5~\text{cm}^2\)