Final answer:
To calculate the percent uncertainty in the area of a circle, you need to know the uncertainty in the radius (Δr). If Δr is given, multiply the percent uncertainty in the radius by 2 to find the percent uncertainty in the area, as the area is proportional to the square of the radius.
Step-by-step explanation:
To calculate the percent uncertainty in the area of a circle, we first need to understand that the uncertainty in the area is dependent on the uncertainty in the radius. Since the area of a circle (A) is given by the formula A = πr², the percent uncertainty in the radius will affect the area by twice its value (because the radius is squared).
Unfortunately, the uncertainty in the radius is not given in the question. Assuming that you might have been provided with this in a different part of the question, let's call this uncertainty Δr. The formula for the percent uncertainty in the radius would then be (% uncertainty in r) = (Δr / r) × 100%. To find the uncertainty in the area, we would then multiply the percent uncertainty in the radius by 2 (since the radius is squared in the area formula) to get the percent uncertainty in the area.
For example, if the percent uncertainty in the radius is 0.5%, the percent uncertainty in the area would be (0.5% × 2) = 1%. However, without the actual value of Δr, we cannot provide the specific percent uncertainty for the area of a circle with a radius of 1.8 x 104 cm.