A sector of a circle of 7cm subtend angle 270 degree at the center calculate the perimeter of the sector

Answer 1

To calculate the perimeter of the sector, we need to find the arc length and the two radii (which are equal in a circle) that make up the perimeter.

Given:
Radius (r) = 7 cm
Angle at the center (θ) = 270 degrees

We know that the circumference of the full circle is 2πr. Since the sector is 270 degrees out of 360 degrees, the arc length of the sector would be:
Arc length = (θ/360) * 2πr
Arc length = (270/360) * 2π(7)
Arc length = (3/4) * 2π(7)
Arc length = 1.5π * 7
Arc length = 10.5π cm

The perimeter of the sector is the sum of the arc length and the two radii:
Perimeter = Arc length + 2r
Perimeter = 10.5π + 2(7)
Perimeter = 10.5π + 14
Perimeter ≈ 45.49 cm

Therefore, the perimeter of the sector is approximately 45.49 cm.