Final answer:
To find a circle's area, use A = πr² if given the radius. If given the diameter, divide it by two to get the radius first, then apply the area formula. The result should have the same number of significant figures as the input with the fewest.
Step-by-step explanation:
When finding the area of a circle, the process differs slightly depending on whether you're given the radius or the diameter. If the radius (r) is given, you use the formula A = πr² to calculate the area. If the diameter (d) is provided, you must remember that the diameter is twice the radius (d = 2r), so you would first divide the diameter by 2 to find the radius and then apply the formula for the area using the newly calculated radius.
For example, if the radius is 2.0 m with only two significant figures, the area will also be reported with two significant figures: A = π(2.0 m)² = 4.5 m². This makes use of the rule that the result of a multiplication or division should have the same number of significant figures as the starting value with the fewest significant figures.
In conclusion, whether you have the radius or the diameter, the key is to use the radius in the area formula. The only additional step when having the diameter is to divide it by two to obtain the radius before using the area formula.