Final answer:
The approximate area of the shaded region of the larger circle is calculated by finding the difference between the area of the larger circle (78.54 m²) and the smaller circle (19.63 m²), which results in about 59 m² after rounding to two significant figures.
Step-by-step explanation:
To calculate the area of the shaded region of the larger circle, we need to find the area of the larger circle and subtract the area of the smaller circle that is inside it. The area of a circle is given by the formula A = πr², where A is the area and r is the radius of the circle.
The radius of the larger circle is 5 meters, so its area is A = π(5 m)² = π(25 m²) = 78.54 m² (rounded to two significant figures).
The radius of the smaller circle is 2.5 meters, so its area is A = π(2.5 m)² = π(6.25 m²) = 19.63 m² (rounded to two significant figures).
The approximate area of the shaded region is the difference between the areas of the two circles: 78.54 m² - 19.63 m² = 58.91 m², which is about 59 m² when rounded to two significant figures.