Created by Hanna Pamuła, PhD candidate Show
Reviewed by Bogna Szyk and Jack Bowater Last updated: Aug 27, 2022 With this sector area calculator, you'll quickly find any circle sector area, e.g., the area of semicircle or quadrant. In this short article we'll:
What is a sector of a circle? Sector definitionSo let's start with the sector definition - what is a sector in geometry? A sector is a geometric figure bounded by two radii and the included arc of a circle Sectors of a circle are most commonly visualized in pie charts, where a circle is divided into several sectors to show the weightage of each segment. The pictures below show a few examples of circle sectors - it doesn't necessarily mean that they will look like a pie slice, sometimes it looks like the rest of the pie after you've taken a slice: You may, very rarely, hear about the sector of an ellipse, but the formulas are way, way more difficult to use than the circle sector area equations. Sector area formulaThe formula for sector area is simple - multiply the central angle by the radius squared, and divide by 2:
But where does it come from? You can find it by using proportions, all you need to remember is circle area formula (and we bet you do!):
The same method may be used to find arc length - all you need to remember is the formula for a circle's circumference. 💡 Note that
Special cases: area of semicircle, area of quadrantFinding the area of a semicircle or quadrant should be a piece of cake now, just think about what part of a circle they are!
Sector area calculator – when it may be useful?We know, we know: "why do we need to learn that, we're never ever gonna use it". Well, we'd like to show you that geometry is all around us:
Apart those simple, real-life examples, the sector area formula may be handy in geometry, e.g. for finding surface area of a cone. Hanna Pamuła, PhD candidate Arc lengthArea of a circleCircle calc: find c, d, a, r… 5 more What is the radius of a circle whose equation is x2 y2 8x − 6y 21 0 2 units 3 units 4 units 5 units?The radius of a circle whose equation is x2 + y2 + 8x - 6y + 21 = 0 is 5units.
What is the area of the sector whose diameter is 40 mm and angle is 120?Therefore,area of sector is 419. 04 mm².
What is the area of the sector if the diameter is 12 cm and the angle is 60?60°360°×π(12)2=24π cm2.
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