Concept 11.4
Major Sectors: Use What's Left
Source: NCERT Mathematics, Class 106 minute lesson
Formal statement
The major sector has angle 360° − θ, so its area is ((360 − θ)/360) × πr². Equivalently, major sector = area of the circle − minor sector.
The intuition
The same two radii split the circle into two sectors: the small one with angle θ and the big one with angle 360° − θ.
So once you know the minor sector, the major one is whatever is left of the circle. For θ = 90°, the major sector is three quarters of the circle.
The attention
Look at the angle that's left over: 360° − θ.
Major sector = (360 − θ)/360 × πr² not θ/360 × πr²
Look hereNot here
- Look here
- The rest of the circle, 360° − θ. The major sector's angle is everything the minor one doesn't use.
- Not here
- The minor sector's share. θ/360 gives the small slice. The question asks for the big one.
- What it teaches
- Sometimes the easiest way to find a big piece is to subtract the small piece from the whole.