mathematical value of the area is known since the days of ancient Greece.Back in those days the Greeks found that the area is a solid part of the surface, which is bounded on all sides by a closed loop.This numerical value, which is measured in square units.The area is a numerical characteristic of flat geometric shapes (planimetric) and the surfaces of bodies in space (volume).
Currently, she is found not only in the school curriculum at lessons of geometry and mathematics, but also in astronomy, life, construction, engineering development, manufacturing and many other areas of human activity.Very often, to calculate the area of the segments we use in the garden landscape design in the zone or during repair work ultramodern design space.Therefore, knowledge of methods of calculating the area of various geometric shapes will be useful anytime and anywhere.
To calculate the area of a circular segment and a segment of a sphere is necessary to deal with the geometric terms, which are needed in the computation process.
First, a fragment is called segment of a circle plane shape of a circle which is situated between the circular arc and its chord cutoff.You should not confuse this concept with the figure of the sector.These are completely different things.
Haarde called the segment that connects the two points on the circle.
central angle formed between the two segments - radii.It is measured in degrees of arc, which abuts.
segment of a sphere is formed by cutting off a plane of the ball (sphere).This base spherical segment turns circle and the perpendicular height is coming from the center of the circle to the intersection with the surface of the sphere.This point of intersection is called the vertex of the segment of the ball.
In order to determine the area of a spherical segment, you need to know the circumference of a circle clipped and height of the ball.The product of these two components will be the area of a spherical segment: S = 2πRh, where h - height of segment, 2πR - circumference, and R - radius of the large circle.
To calculate the area of a circle segment, you can resort to the following formulas:
1. To find the area of a segment in the simplest way, you need to calculate the difference between the area of the sector, which is inscribed in the segment, and the area of an isosceles triangle whose base ischord segments: S1 = S2-S3, where S1 - area of the segment, S2 - area sector and S3 - the area of a triangle.
can use the approximate formula for calculating the area of a circular segment: S = 2/3 * (a * h), where a - the base of a triangle or a chord length, h - the height of the segment, which is the result of the difference between the radius of the circle and the height of an isosceles triangle.
2. The area of the segment is different from the semi-circle, is calculated as follows: S = (π R2: 360) * α ± S3, where π R2 - area of a circle, α - degree measure of central angle that contains an arc segment of a circle,S3 - the area of a triangle that is formed between two radii of a circle and a chord of owning an angle at the center point of the circle and two vertices at the point where the radii of the circle.
If the angle α & lt;180 degrees, use a minus sign if α & gt;180 degrees, use the plus sign.
3. Calculate the area of the segment can be, and other methods using trigonometry.As a rule, the basis of a triangle.If the central angle is measured in degrees, is acceptable then the following formula: S = R2 * (π * (α / 180) - sin α) / 2, where R2 - square radius of the circle, α - degree measure of central angle.
4. To calculate the area of a segment using trigonometric functions can use a different formula and with the proviso that the central angle is measured in radians: S = R2 * (α - sin α) / 2, where R2 - square radius of the circle, α -degree measure of central angle.
