Final answer:
A radius is half the length of the diameter of a circle. For a circle with a diameter (d), the radius (r) can be calculated as r = d/2. This measurement is crucial in determining circular path properties such as arc length and area of the circle.
Step-by-step explanation:
A radius is half the length of the diameter of a circle. In mathematical terms, if the diameter (d) of a circle is the distance across the circle through its center, then the radius (r) is half that distance or r = d/2.
The concept of a radius is fundamental in understanding circular motion as well.
For instance, the arc length (As) traveled along a circular path can be determined if you have the radius and the angle of rotation. The radius is important because it also relates to the radius of curvature, which is, simply, the radius of a circular path.
To give a practical example, let's calculate the area (A) of a circle with a radius of 1.2 meters:
A = πr² = (3.1415927...) × (1.2 m)² = 4.5238934 m²
However, due to the significant figures rule, this would be rounded to: A = 4.5 m²