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measure of central angle/360 degrees = area of sector/area of circle

110 degrees/360 degrees = 40 unit2/ pi r2 unit2

11/36 = 40/pi r2

11 pi r2 = 40 x 36

11 pi r2 = 1,440

r2 = 1,440/11 pi

r = square root of 1,440/11 pi

r = 20.3 unit approximately

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Q: The area of the sector formed by the 110 degree central angle is 40 units squared What is the radius of the circle?
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The area of the sector formed by the 110 degree central angle is 50 units squared What is the circumference of the circle?

For A+ 7.22The area of a sector of a circle is proportional to the angle at the center of the sector, with 360 degrees corresponding to the full circle. Therefore, the area of the total circle for which the problem is stated is 50 X 360/110 = about 163.6 square units. The area of a circle is also equal to pi multiplied by the square of the radius of the circle, so that the radius r of this circle equals the square root of 163.6/pi = about 7.217 units. The circumference of the circle is also twice the radius multiplied by pi = 45 units, to the justified number of significant digits (limited by "50").a+ 45.33


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A central angle.The section of the circle formed by that angle and the part of the circle (the part being the circumference) between the radii is called a sector.


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A circle contains 360 degrees. Draw a circle, add a radius to any point on it, and then rotate the radius completely around. After it has returned to the point it initially intersected the curve, the radius will have rotated through 360 degrees.(another explanation, maybe no better.)A complete circle measures 360 degrees, so a half-circle is 180 degrees, a quarter-circle is 90 degrees and so forth. Another way to look at it is in terms of the central angle formed by the radii drawn from each endpoint of the arc - the measure of the arc in degrees is the same as the measure of this central angle in degrees.


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A quarter of a circle, formed by two radii forming a right angle at the centre, is called a quadrant.

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