Question

A sector of a circle of radius 6cm subtends angle of 105 at the centre of the circle calculate the perimeter

Answer 1

The perimeter of the sector is the sum of the arc length and the lengths of the two radii forming the sector.

The length of the arc is calculated using the formula:

arc length = (angle in degrees/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:

arc length = (105/360) x 2π x 6
arc length = (7/24) x 12π
arc length = 7π/2

The lengths of the two radii forming the sector are each equal to the radius of the circle, which is 6cm.

Therefore, the perimeter of the sector is:

perimeter = arc length + 2(radius)
perimeter = 7π/2 + 2(6)
perimeter = 7π/2 + 12
perimeter ≈ 24.64cm (rounded to two decimal places)