Final answer:
The change in area resulting from increasing the radius from 6.00 m to 6.02 m is approximately 0.637 m², which is about 0.56% of the circle's original area. This illustrates the sensitivity of the circle's area to changes in the radius because the area formula depends on the square of the radius.
Step-by-step explanation:
When the radius of a circle is increased from 6.00 m to 6.02 m, we can estimate the resulting change in area by first applying the formula for the area of a circle, A = πr². The original area is π(6.00 m)² and the new area is π(6.02 m)². Using a calculator with an eight-digit output, this gives us:
The change in area, therefore, is approximately 113.734 m² - 113.097 m² = 0.637 m². To calculate the percentage change in area, we take the change in area divided by the original area and multiply by 100:
Percentage change in area = (0.637 m² / 113.097 m²) × 100 ≈ 0.56%
The sensitivity of the area to changes in radius can be analyzed by noting that a small change in radius results in a relatively larger change in area, which is a result of the area formula being a square relationship with the radius. This means that the geometric implication of increasing the radius is that the area increases by the square of the change in the radius, although this change might appear small when looking at the radii alone.