1. **Problem 1:** Calculate the distance from the surface to the centre of the Earth given the Earth's circumference is 40000 km.
2. The formula relating circumference $C$ and radius $r$ of a circle is:
$$C = 2\pi r$$
3. Rearranging to find the radius:
$$r = \frac{C}{2\pi}$$
4. Substitute $C = 40000$ km:
$$r = \frac{40000}{2 \times 3.1416} = \frac{40000}{6.2832} \approx 6366.2 \text{ km}$$
5. So, the distance from the surface to the centre of the Earth (the radius) is approximately $6366$ km.
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6. **Problem 2:** Calculate the total length of 28 coins laid end to end, each with circumference 5.1 mm, and give the answer in centimetres.
7. Since the coins are laid flat end to end, the length of each coin is equal to its diameter.
8. The diameter $d$ is related to circumference $C$ by:
$$d = \frac{C}{\pi}$$
9. Calculate diameter of one coin:
$$d = \frac{5.1}{3.1416} \approx 1.623 \text{ mm}$$
10. Total length for 28 coins:
$$28 \times 1.623 = 45.444 \text{ mm}$$
11. Convert mm to cm:
$$45.444 \text{ mm} = \frac{45.444}{10} = 4.5444 \text{ cm}$$
12. Final answer: The total length of the line of coins is approximately $4.54$ cm.
Earth Radius Coins Length
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