What is the length of a 45° arch on a radius of a circle in 10 km?
To find the length of a 45° arch on a circle with a radius of 10 km, we need to use the formula for the circumference of a circle.
The formula for the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius.
Plugging in the given radius of 10 km into the formula, we have C = 2π(10) = 20π km.
Since the 45° arch is only a fraction of the full circumference, we need to find the length of this fraction.
The length of a given fraction of the circumference is calculated by multiplying the fraction by the full circumference.
The fraction of a circle represented by a 45° arch is 45/360 or 1/8.
Therefore, the length of the 45° arch on a radius of 10 km is (1/8) * 20π km, which simplifies to 5π km.
Rounded to the nearest whole number, the length of the 45° arch is approximately 15.71 km.