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?

Answer: 87.9 cm2

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.

Answer: 38.7 cm

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

Arc Length = `frac(70)(360)` x 75.36

Arc Length = 14.65 cm

Perimeter = 14.65 + 12 + 12 = 38.65 cm