1. Calculate the circumference and the area of a circle with: a) radius 83 cm b) diameter 257 mm .

To calculate the circumference and area of a circle, we can use the following formulas: 1. **Circumference (C)**: \[ C = 2\pi r \] where \( r \) is the radius. 2. **Area (A)**: \[ A = \pi r^2 \] ### a) For a circle with a radius of 83 cm: 1. **Circumference**: \[ C = 2\pi(83) \approx 2 \times 3.14159 \times 83 \approx 521.6 \text{ cm} \] 2. **Area**: \[ A = \pi(83^2) \approx 3.14159 \times 6889 \approx 2168.8 \text{ cm}^2 \] ### b) For a circle with a diameter of 257 mm: First, we need to find the radius: \[ r = \frac{d}{2} = \frac{257 \text{ mm}}{2} = 128.5 \text{ mm} \] 1. **Circumference**: \[ C = 2\pi(128.5) \approx 2 \times 3.14159 \times 128.5 \approx 808.5 \text{ mm} \] 2. **Area**: \[ A = \pi(128.5^2) \approx 3.14159 \times 16512.25 \approx 51800.5 \text{ mm}^2 \] ### Summary of Results: - For a circle with a radius of 83 cm: - Circumference: approximately **521.6 cm** - Area: approximately **2168.8 cm²** - For a circle with a diameter of 257 mm: - Circumference: approximately **808.5 mm** - Area: approximately **51800.5 mm²**