Final answer:
The relationship between the circumference of a circle and its radius is described by the formula C = 2πr, and the area of a circle is given by A = πr².
The number π (pi) is approximately 3.14159, and using these formulas, you can calculate both circumference and area, considering the radius is given with significant figures.
Step-by-step explanation:
The formula that justifies the relationship between the circumference (C) and the radius (r) of a circle is given by:
A) C = 2πr, A = πr²
This means the circumference of a circle is 2 times π times the radius, and the area (A) of a circle is π times the square of the radius. This formula corresponds with the knowledge used by the ancient Greeks and is still valid. The ancient Greeks knew that the length of a circle, or the circumference, was 2πr, which is somewhat close to 6 times the radius, since the diameter (2r) fits across a square and thus, the perimeter of the circle would be smaller than the square's perimeter (4 times the side length).
For example, using a specific radius, if the radius (r) is 1.2 meters, the area (A) calculated to two significant figures would be A = πr² = (3.1415927...) × (1.2 m)² = 4.5238934 m², which rounds to 4.5 m² due to the significant figures rule.