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In this circle, the area of sector COD is 50.24 square units.
The radius of the circle is ____ units, and mAB is ____ units.

In This Circle The Area Of Sector COD Is 5024 Square Units The Radius Of The Circle Is Units And MAB Is Units class=

Sagot :

rvkacademic

Answer:

Radius = 8 units

Length of arc AB = 8.37758 units

Step-by-step explanation:

The sector COD is 1/4 the size of the circle.

the vertex angle is 90° and a circle has 360° at the center.

So the area of sector COD/area of Circle = 90/360 = 1/4

This means the area of the circle is 4 * 50.24 = 200.96 square units

Area of circle = πr² where r is the radius
πr² = 200.96

r² = 200.96/ π = 63.9676 ≅ 64
Therefore r = √64 = 8 units

The circumference of the circle is 2πr = 16π units

arc AB has a vertex angle of 30°.

30°/360° = 1/6

So the length of the arc is 1/6th the circumference of the circle =

(1/6) * 16π  = 2.67π  units or 8.37758 units

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