The radius and diameter are terms related to geometric shapes, especially circles and spheres. Here’s an explanation of each one:

• Radius:
  • The radius is the distance from the center of a circle or sphere to any point on its circumference or surface.
  • In other words, it’s the line segment that connects the center of the circle or sphere to any point on the edge or surface.
  • Mathematically, if the radius of a circle is known, several properties of the circle, such as its area or circumference, can be calculated.
• Diameter:
  • The diameter is twice the radius. That is, it’s the longest distance you can measure across a circle, passing through its center.
  • The diameter connects two points on the circumference of a circle, passing through the center.
• Relationship Between Radius and Diameter:
  • As mentioned before, the diameter is always twice the radius. This means that if you know the radius of a circle, you can calculate the diameter by multiplying the radius by 2.
  • Conversely, if you know the diameter, you can obtain the radius by dividing the diameter by 2.

Example:

• If a circle has a radius of 5 cm, its diameter will be $2 \times 5 = 10$ cm.
• If the diameter of a circle is 12 cm, the radius will be $12 / 2 = 6$ cm.

In summary, the radius is half of the diameter, and both are fundamental for calculating other properties of a circle or sphere, such as area or volume (in the case of spheres).