A sector of a circle of a radius 6cm subtends angle of 105 at the centre of the circle calculate the perimeter of the sector
The perimeter of a sector is equal to the length of the arc plus the length of the two radii.
To find the length of the arc, we need to use the formula:
length of arc = (angle/360) x 2πr
where r is the radius of the circle.
In this case, the angle is 105 degrees and the radius is 6cm, so:
length of arc = (105/360) x 2π(6) = 3.5π
To find the length of the two radii, we can simply multiply the radius by 2:
length of two radii = 2 x 6 = 12
Therefore, the perimeter of the sector is:
perimeter = length of arc + length of two radii
perimeter = 3.5π + 12
Using a calculator, we can approximate this to:
perimeter ≈ 26.71cm (rounded to two decimal places)