Final answer:
The area of a quarter circle with a radius of 1 kilometer is 0.785398 km², calculated by dividing the area of the full circle (π km²) by 4.
Step-by-step explanation:
To calculate the area of a quarter circle when the radius is 1 kilometer, you can start by calculating the area of a full circle using the formula A = πr², where π is approximately 3.14159 and r is the radius of the circle.
For a full circle with a radius of 1 kilometer, the area is A = π(1 km)² = π km².
Since we want the area of a quarter circle, we divide the area of the full circle by 4, which gives us π km² / 4 = 0.785398 km² (to the nearest six decimal places).