Final answer:
The length of the 45° arc is 7.85 centimeters.
Step-by-step explanation:
The radius of a circle is 10 centimeters, and we want to find the length of a 45° arc. To solve this, we'll use the fact that the arc length (δs) for an angle of rotation (δθ) is proportional to the angle of rotation.
Specifically, the arc length is found by dividing the angle of the circle by 360° and multiplying by the circumference of the circle (2πr).
For a 45° arc, the calculation becomes: δs = (45°/360°) × (2π × 10 cm), which simplifies to: δs = (1/8) × (20π cm), or δs = 2.5π cm.
Length of Arc = (45/360) x (2 x 3.14 x 10) = 0.125 x 62.8 = 7.85 centimeters
Therefore, the arc length for a 45° arc in a circle with a radius of 10 cm is approximately 7.85 cm (using 3.14 as the approximation for π).