Final answer:
The exact area of a circle with a radius of 10cm is 314.15927... cm². However, considering significant figures, the approximate area reported to two significant figures is 310 cm².
Step-by-step explanation:
The question asked pertains to finding the approximate area and the exact area of a circle with a given radius. Since the radius provided is 10 centimeters, the area formula that will be applied is A = πr², where π is Pi (approximately 3.1415927...) and r is the radius of the circle.
To determine the exact area of the circle, we apply the formula directly: A = π * (10 cm)² = 3.1415927... * 100 cm² = 314.15927... cm². As for the approximate area, we typically round Pi to a reasonable degree of precision, often to two decimal places, thus using 3.14 instead of its extended form. This provides an area of roughly A ≈ 3.14 * 100 cm² = 314 cm².
However, the concern about significant figures arises in a more accurate context. If we wish to limit our result to the same number of significant figures as the given radius (two significant figures), the most precise approximate area we should report is 310 cm², considering that the second digit after the decimal point will be rounded down.