The ratio of the sector area to the area of the entire circle can be expressed by the formula:
Ratio = (Area of the Sector) / (Area of the Circle)
The area of the entire circle is calculated using the formula:
Area of Circle = πr²
where r is the radius of the circle. On the other hand, the area of a sector can be calculated with:
Area of Sector = (θ / 360) × πr²
where θ is the angle of the sector in degrees. By substituting the formula for the area of the sector into the ratio, we get:
Ratio = [(θ / 360) × πr²] / [πr²] = θ / 360
This means that the ratio of the area of the sector to the area of the entire circle is simply the angle of the sector divided by 360 degrees. This ratio tells us what fraction of the circle’s area is taken up by the sector.