Question

the perimeter of a sector of a circle of radius 10cm is (pie + 20cm.calculate the angle of the sector​

Answer 1

18

Explanation:

Perimeter of sector of circle = radius + radius + length of arc.

`\pi + 20 = 10 + 10 + length \: of \: arc \\ length \: of \: arc \: = \pi + 20 - 20 = \pi`

So how do we calculate length of arc?

Length of arc is obtained by the following formula:

`length \: of \: arc \: = (angle)/(360) * 2 \: \pi \: r \: \\ (angle)/(360) * 2\pi(10) = \pi \\ (angle)/(360) * 20\pi = \pi \\ (\pi * angle)/(18) = \pi \\`

(cross multiply them)

`\pi * angle = 18 \: \pi \\ angle \: = (18\pi)/(\pi) = 18`

Angle = 18