Circles - Arcs Sectors

# Circles - Arcs Sectors

GCSE(F), GCSE(H),

An arc is part of the circumference of a sector. The amount of the circumference that is described is given by the number of degrees at the centre.

The arc length is a fraction of the circumference of the circle. The circumference of the whole circle is given by 2pir, and the angle at the centre is 360º. The angle of the arc is 83º, or frac(83)(360) of a whole circle:

The arc length is therefore frac(83)(360)pir.

If the perimeter of the arc is required, include the two radii: frac(83)(360)pir + 2.

The area of a whole circle is pir^2. The area of a sector is the same fraction: frac(83)(360)pir^2.

## Examples

1. What is the area of the sector, shown below?

Area = frac(70)(360)πr2

A = frac(70)(360)πx 122

A = 87.92 cm2

2. What is the length of the perimeter of the sector shown below? give the answer to 1 decimal place.

Arc Length = frac(70)(360) x 2 x π x r
Arc Length = frac(70)(360) x 75.36