Final answer:
The area of a circle with a radius of 4.1 km is calculated using the formula A = πr². The final result, respecting significant figures, is 53 km².
Step-by-step explanation:
To find the area of a circle with a radius of 4.1 km, use the formula A = πr², where A is the area and r is the radius of the circle. The approximate value of π (pi) is 3.1415927. Plugging the radius into the formula, we get:
A = π(4.1 km)²
π is a constant and the radius should be squared, then multiplied by π:
A = 3.1415927 × (4.1 km) × (4.1 km)
A = 3.1415927 × 16.81 km²
π is precise to many decimal places but the radius given (4.1 km) has only two significant figures, so the area should be reported with the same number of significant figures. By carrying out the multiplication, we get:
A = 52.8109501 km² (which is the precise calculation)
However, to respect the significant figures, we round the area to:
A = 53 km²