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Jetzt kostenlos anmeldenA segment of a circle is the area defined by a line from one side of the circumference to the other.
Segments are divided into major and minor segments:
Major segments are the larger proportion of the circle.
Minor segments are the smaller proportion of the circle.
When working with the area of a segment of a circle, you should always remember the formula for the area of a circle: . This is the formula you use regardless of whether the angle is in radians or degrees.
When working out the area or circumference of a segment of a circle, the angle at the centre of the circle which defines the segment can be in either radians or degrees.
To find the area of a segment of a circle (the blue part), you need to know the angle at the centre where the radii brackets the chord (x) and the radius:
To find the area of a minor segment of a circle when the angle at the centre (x) is in radians, the formula is:
To find the area of a major segment of a circle when the angle at the centre is in radians, the formula is:
Instead of trying to remember both formulas, it might be easier to remember the area of the major segment formula as a word equation:
Circle A has a minor segment which is highlighted in pink.
Minor segment = 7.64 square units (3 sf)
b. Finding the area of the major segment
To check, if you add both the minor and major segments together, you should get approximately the same as the area of the whole circle . Here, and minor segment + major segment = .
You still need to know the radius and the centre of the circle, but there is now a different formula.
The formula to find the minor segment of a circle, when the angle at the centre (x) is in degrees:
To find the major segment of a circle when the angle at the centre (x) is in degrees, the formula is:
Use the same principle as when the angle is in radians – you need to minus the minor segment from the whole area of the circle.
Circle B has a minor segment, and the angle at the centre defines the length of the segment. The angle is and the radius is 10 cm.
a. Finding the minor segment of Circle B.
Identify all the key information required to calculate the area. Radius = 10 cm; angle at the center =
Substitute into the formula
Minor segment = 75.7 square units (3 sf)
b. Finding the major segment of Circle B.
Major segment = 239 square units (3 sf)
The method to calculate the arc length of a segment is the same for calculating the arc length of a sector.
A segment in Circle C has a radius of 7 cm with an angle of . What is the arc length of this segment?
A segment in Circle D has a radius of 5 cm with an angle of . What is the arc length of this segment?
A segment of a circle is the area of a proportion of a circle between a chord and the circumference. Segments can either be minor (the small part) or major (the larger part).
Finding the area of a segment of a circle can be found by substituting your values into a formula, which formula you use depends on whether the angle at the centre which defines the segment is in radians or degrees.
The area of a segment of a circle can be broken down into major (the larger proportion) and minor (the smaller proportion). When you use the area of a segment of a circle formulas, you are calculating the minor segment area. To calculate the major area, you need to subtract the minor segment area away from the area of the circle.
There are two formulas for finding the area of a minor segment of a circle. If the angle at the centre of the circle which defines the chord is in radians, then the formula you use is 1/2 × r ^ 2 × (x-sin (x)). If the angle at the centre is in degrees, you use ((X× pi)/360 - sinx/2)× r ^ 2
What is a segment?
A segment of a circle is the area defined by a line from one side of the circumference to the other.
What is a minor segment?
The smaller proportion of a circle which is defined by a chord
What is a major segment?
The larger proportion of a circle which is defined by a chord.
There are two formulas you can use to calculate the area of a segment. What decides which one you use?
The units of the angle at the centre of the circle- whether they are in radians or degrees.
How do you calculate the area of the major segment of the circle?
The area of the circle - the area of the minor segment.
Circle A has a minor segment whereby the angle at the centre which defines the length of the segment is 100o and a radius of 9. What is the area of the minor segment of Circle A?
91.2 (3 s.f)
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