Question

The diagram shows a sector of a circle radius 10cm

calculate the perimeter of the sector
give answer to 1 decimal place

Answer 1

`\text{Perimeter of sector = 43.6 (Rounded to the nearest tenth.)}`

Explanation:

`\text{Perimeter of the sector = Radius + arc length + radius}`

`\text{Radius = 10 cm}`

`\text{Perimeter of the sector = 10 + arc length + 10 }`

`\text{Perimeter of the sector = 20 + arc length }`

`\text{arc length = (sector angle/ 360 ) * perimeter of the circle}`

`\text{Perimeter of a circle }=2\pi r`

`\text{sector angle} = 135`

`\text{arc length} = (135/ 360 ) * 2\pi (10)`

`= (3/8) 20\pi`

`= 15\pi /2`

`\text{Using }\pi =3.14`

`= 15 * 3.14 /2`

`= 23.55`

`\text{Perimeter of the sector = 20 + 23.55}`

`= 43.55`

`= 43.6 cm`

`\text{perimeter of the sector = 43.6 cm }`