Final answer:
The area of a circle with a radius of 10 meters, calculated with the formula A = πr², is approximately 314 square meters when rounded to two significant figures.
Step-by-step explanation:
To find the area of a circle with a radius of 10 meters, we use the formula A = πr². Plugging in the radius, we calculate the area as A = 3.1415927 × 10² square meters. However, since the radius was given with only two significant figures, our answer should also reflect two significant figures for precision. Therefore, the area of the circle is approximately 314 square meters when rounded to two significant figures.
It's important to remember that when performing calculations, the number of significant figures in the result should match the starting value with the fewest significant figures. This helps maintain the integrity of the precision in our measurements. Additionally, understanding the concept of significant figures aids in making mathematical sense of understandings, such as recognizing that a circle's area is less than the area of a square circumscribing it.