How To Find The Radius Of A Semicircle

Explore this collection of circle facts. Learn how to detect the circumference, diameter, radius, and area of a circumvolve and go definitions of circle terms used in geometry.

Circle Facts

A circle is a two-dimensional shape formed by all the points that are the same altitude from a heart point.
Technically, only the points equidistant from the centre class the circumvolve. The area enclosed within a circle is chosen a disc.
The word circle comes from the Greek word κρίκος (krikos), meaning "hoop" or "band".
A circle is the only 1-sided shape containing an area. A straight line is a circumvolve containing an infinite area.
Humans have recognized circles since ancient times. Natural circles include the shapes of the Sun and Moon, the human eye, tree cross-sections, some flowers, some shells, etc.
The altitude effectually a circle is its circumference.
The altitude from the centre to the circle is its radius.
The longest altitude betwixt two points on a circle is the diameter, which is a line segment running through the eye.
A circle is the shape with the shortest perimeter enclosing an area.
The circle is the about symmetric shape because every line through the center is a line of reflection symmetry. It has rotation symmetry for every angle around its center.
Pi (π) is an irrational number that is the ratio of a circumvolve's circumference to its diameter. It is approximately equal to three.1415259.
Archimedes proved the area enclosed inside a circle is the same as the surface area of a triangle with a base the length of the circle's circumference and height equal to the circumvolve'southward radius.
The total arc of circle measures 360 degrees.
A circumvolve is a special type of ellipse where the two foci are in the same location and the eccentricity is 0.
Written in 1700 BCE, the Rhind papyrus describes a method of finding the area of a circle. The result comes out every bit 256/81, which is near iii.xvi (close to pi).
You lot can draw a special circumvolve inside every triangle, called the incircle, where each of the iii triangle sides are tangent to the circumvolve.

How to Find the Circumference of a Circle

The circumference (C) is the distance around a circle. There are a few ways to find the circumference. You can calculate it from either the radius (r) or diameter (d) or you tin can mensurate it.

C = 2πr
C = πd
It'south easiest to measure a circle's circumference using a cord. Shape the string around the circle, mark the length, and and so use a ruler or meter stick to measure the length of the cord.

How to Observe the Diameter of a Circumvolve

The diameter (d) is the length of the line segment with end points on the circle that passes through its middle. It is the longest distance beyond a circle. The diameter is twice the length of the radius.

d = 2r
d = C/π
Measure the diameter by finding the longest line segment beyond a circle.

How to Find the Radius of a Circle

The radius (r) is the distance from the center of a circle to its border. Information technology is half the length of the diameter.

r = d/2
r = C/2π
If you draw a circle using a compass, the radius is the distance between its two points. Measuring the radius of a circle is a bit tricky unless you know its centre. Sometimes its easier to measure the circumference or diameter and calculate the radius.

How to Discover the Surface area of a Circle

The expanse (A) of a circle is the region enclosed past a circumvolve or the expanse of its disc.

A = πr²
A = π(d/2)²
A = Cr/2 – You can use Archimedes' proof to find the circle area using its circumference and radius. Set the base of the triangle equal to circumference C and height equal to radius r. The triangle area formula i/2 bh becomes A = Cr/2

Circumvolve Vocabulary Terms

Hither are central circle vocabulary terms to know:

Annulus: An annulus is a ring-shape formed between 2 concentric circles.
Arc: An arc is whatsoever segment of a circumvolve formed past connected points.
Center (Heart): The middle is the point that is equidistant from all points on a circumvolve. Information technology is also called the origin.
Chord: A chord is a line segment with endpoints on the circle. The diameter is the longest chord.
Circumference: The circumference is the distance effectually a circle.
Closed: A region that includes its boundaries.
Diameter: The diameter is the line segment with endpoints on the circle and midpoint at its center. It is the largest distance betwixt any two points on a circumvolve.
Disc: A disc is the area inside a circumvolve.
Lens: A lens is a region shared past two overlapping discs.
Open: Whatsoever region, excluding its boundaries.
Passant: A passant is a coplanar line that has no points in common with a circle.
Radius: A radius is a line segment running from the center to the circumvolve.
Sector: A sector is an area within a circle bounded by 2 radii.
Segment: A segment is an area bounded past an arc and a chord.
Secant: A secant is a chord that extends across the circle. In other words, it is a coplanar line that intersects a circumvolve at 2 points.
Semicircle: A semicircle is an arc which has the bore as endpoints and center as midpoint. The interior of a semicircle is a half-disc.
Tangent: A tangent is a coplanar line sharing one single bespeak in mutual with a circle.

References

Gamelin, Theodore (1999). Introduction to Topology. Mineola, N.Y: Dover Publications. ISBN 0486406806.
Harkness, James (1898). "Introduction to the theory of analytic functions". Nature. 59 (1530): 30. doi:ten.1038/059386a0
Katz, Victor J. (1998). A History of Mathematics / An Introduction (2nd ed.). Addison Wesley Longman. ISBN 978-0-321-01618-8.
Ogilvy, C. Stanley (1969). Excursions in Geometry. Dover.