Final answer:
The diameter of a circle is double the radius, represented by the equation D = 2r, while the radius is half of the diameter, given by r = D/2. Multiplication or division by 2 is used to convert between these two measurements.
Step-by-step explanation:
To find the diameter of a circle when given the radius, you simply multiply the radius by 2. The diameter (D) is twice the length of the radius (r), so the equation is D = 2r. For example, if the radius is 5 units, the diameter would be 5 units × 2 = 10 units.
Conversely, to find the radius given the diameter, you divide the diameter by 2. The equation is r = D/2. If the diameter of a circle is 12 units, then the radius is 12 units ÷ 2 = 6 units.
Remembering that the perimeter (or circumference) of a circle is 2πr, where π is approximately 3.14159, can also help reinforce the relationship between radius and diameter. For instance, with a radius of 4 units, the circumference would be 2 × 3.14159 × 4 units = 25.13272 units, approximately.