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

User Jmagnusson
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1 Answer

4 votes

Answer:

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

User CristianGuerrero
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