Final answer:
The formula for the area of a circle in terms of the radius is A = πr² (Option A). This formula remains unchanged when expressing the area in terms of radius, regardless of the circumference formula. Significant figures in the radius should be considered when presenting the final area.
Step-by-step explanation:
The equation for the circumference of a circle is C = 2πr, where C represents the circumference and r is the radius of the circle. To solve for the radius (r) in terms of the circumference, you would rearrange the formula to get r = C/(2π). Now, by using the formula for the area of a circle, which is A = πr², and substituting r with C/(2π), the formula for the area in terms of the radius is just A = πr² itself, not modified.
Therefore, the correct answer for the formula of the area of a circle in terms of the radius r is A = πr² (Option A). When calculating the area using this formula with a radius given in significant figures, such as r = 1.2 m, it is important to maintain the correct amount of significant figures in the final result. For instance, A = π(1.2 m)² = 4.5238934 m² would be rounded to A = 4.5 m² if the radius is specified with two significant figures.