Circle/Sector Area and Perimeter Calculations A circle is a plane figure with no corners or edges, and its circumference is the length of its perimeter....
A circle is a plane figure with no corners or edges, and its circumference is the length of its perimeter. A sector is a portion of a circle bounded by two radii and the intercepted arc.
Calculating the area of a circle:
The area (A) of a circle is calculated using the formula A = πr², where r is the radius of the circle.
The radius is half the distance from the center to any point on the circle.
For example, if the radius of a circle is 5 cm, the area would be **A = π(5 cm)² = 78.5 cm².
Calculating the perimeter of a circle:
The perimeter (P) of a circle is calculated using the formula P = 2πr.
The perimeter is the length of the circumference of the circle.
Similarly to the area, the circumference can be found by multiplying the radius by 2π.
For example, if the radius of a circle is 5 cm, the perimeter would be P = 2π(5 cm) = 31.4 cm.
Calculating the area of a sector:
The area of a sector can be calculated using the formula A = (θ/360°) × A, where θ is the angle of the sector in degrees and A is the area of the entire circle.
The angle of a sector is the portion of the circle it occupies.
For example, if a sector has an angle of 60°, the area would be **A = (60/360°) × 78.5 cm² = 31.25 cm².
Additional notes:
The area of a circle is always greater than the area of a sector with the same angle.
The perimeter of a circle is always greater than the perimeter of a sector with the same angle.
When dealing with sectors, remember that the angle can be measured in both degrees and radians