Subjects geometry

Earth Sphere

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1. **Problem statement:** Calculate the circumference, surface area, and volume of Earth modeled as a sphere with radius $r = 6.37 \times 10^6$ meters. 2. **Formulas:** - Circumference: $C = 2 \pi r$ - Surface area: $A = 4 \pi r^2$ - Volume: $V = \frac{4}{3} \pi r^3$ 3. **Unit conversion:** Since the radius is in meters, convert it to kilometers by dividing by 1000: $$r = \frac{6.37 \times 10^6}{1000} = 6370 \text{ km}$$ 4. **Calculate circumference:** $$C = 2 \pi \times 6370 = 2 \times 3.1416 \times 6370 \approx 40030 \text{ km}$$ 5. **Calculate surface area:** $$A = 4 \pi (6370)^2 = 4 \times 3.1416 \times 40576900 \approx 510064471 \text{ km}^2$$ 6. **Calculate volume:** $$V = \frac{4}{3} \pi (6370)^3 = \frac{4}{3} \times 3.1416 \times 258518213000 \approx 1.08321 \times 10^{12} \text{ km}^3$$ **Final answers:** - Circumference $\approx 40030$ km - Surface area $\approx 5.10 \times 10^8$ km$^2$ - Volume $\approx 1.08 \times 10^{12}$ km$^3$