Final answer:
The length of the arc subtended by a central angle of 315° in a circle with a radius of 4ft is approximately 21.99ft when rounded to the nearest hundredth.
Step-by-step explanation:
The student asked to find the length of the arc subtended by a central angle of 315° in a circle with a radius of 4ft. To find this arc length, we will use the relationship between the arc length (s), the radius (r), and the central angle (Δθ) measured in radians. Since there are 2π radians in a full 360° rotation, a 315° angle corresponds to θ = (315°/360°) × 2π radians = (7π/4) radians.
The formula to calculate the arc length is: s = r×θ. Therefore, the arc length for 315° in a circle with a radius of 4ft is: s = 4ft × (7π/4) = 7π ft. With π approximated to 3.14159, the calculated length is about 7 × 3.14159 = 21.99113ft, which we round to 21.99ft to the nearest hundredth.