Final answer:
The area (A) of a circle with radius (r) is calculated using the formula A = πr². Pi (π) approximates to 3.14159 and for a circle inside a square with a side of 2r, the area is around ⅔3r², which approximates πr².
Step-by-step explanation:
The formula for finding the area of a circle with radius r is A = πr². The Greek letter π (pi) is a mathematical constant approximately equal to 3.14159, representing the ratio of the circumference of a circle to its diameter. When calculating the area of a circle, you multiply pi by the square of the radius.
For example, if you have a circle with a radius of 1.2 meters, using the formula you would calculate the area as A = π(1.2 m)² = 4.5238934 m² using a calculator with eight-digit output. However, since the radius has only two significant figures, the calculated area should also be reported with two significant figures as A=4.5 m².
In the context of a circle fitting inside a square with the relationship a = 2r, the area of the circle would be smaller than the area of the square (which is a²), but likely around three-quarters of the square's area. Using this relationship, we can deduce that the circle's area is approximately 3r², which leads us back to the area formula A = πr².