Question

The cross-section of a gate is a sector of a circle with radius 8.5 m and angle 76°.

Calculate the perimeter of the sector.
Help pls

Answer 1

28.275 m

Explanation:

For a sector with angle α in a circle of radius r, the sector length = α/360 x 2πr where 2πr represents the circumference of the circle

Here r = 8.5 so circumference = 2 x π x 8.5 = 53.407 m

α = 76

So the sector length is 76/360 x 53.407 = 11.275 m

The perimeter will the the length of the sector plus twice the radius so it would be 2r + 11.275

= 2 x 8.5 + 11.275 = 17 + 11.275 = 28.275 m