**Problem 1:** Amy runs around a circular track. 1. a) Find the circumference if 8 laps equal 2000m. 2. b) Find the number of laps if she runs 2500m. 3. c) Find the distance needed to reach 7.5km total after previous runs. **Problem 2:** Given circumference of cycle track is 1500m. --- **Step 1a:** 1. The total distance for 8 laps is 2000m. 2. Circumference $C$ is distance per lap, so $C = \frac{2000}{8} = 250$ meters. **Step 1b:** 1. Given distance run is 2500m. 2. Number of laps $n = \frac{\text{distance}}{\text{circumference}} = \frac{2500}{250} = 10$ laps. **Step 1c:** 1. Total target distance is 7.5 km = 7500 m. 2. Distance already run is $2000 + 2500 = 4500$ m. 3. Remaining distance $= 7500 - 4500 = 3000$ m = 3 km. **Step 2:** 1. Circumference $C = 1500$ m. 2. Using formula $C = 2\pi r$, solve for radius $r$: $$r = \frac{C}{2\pi} = \frac{1500}{2\pi} = \frac{1500}{6.2832} \approx 238.73 \text{ m}$$ 3. Diameter $D = 2r = 2 \times 238.73 = 477.46$ m. --- **Final answers:** - 1a) Circumference = 250 m - 1b) Laps run = 10 - 1c) Distance needed = 3 km - 2) Radius $\approx$ 238.73 m, Diameter $\approx$ 477.46 m