Final answer:
The length of the equator, considering the given Earth's radius of 6400 km, can be calculated using the formula C = 2*pi*r, resulting in an approximate circumference of 40212 km. However, the more precise value of Earth's radius is 6371 km, giving a circumference of about 40030 km.
Step-by-step explanation:
Length of the Equator
The student asked about the length of the equator if the radius of the Earth is 6400 kilometers. To calculate the circumference of the Earth at the equator, we use the formula for the circumference of a circle, which is C = 2πr, where C is the circumference, π (pi) is approximately 3.14159, and r is the radius of the circle. Using the value given for the Earth's radius, we calculate as follows:
- Let r = 6400 km (the given Earth's radius)
- Multiply this radius by 2 to find the diameter of Earth: 6400 km x 2 = 12800 km
- Multiply the diameter by π to find the circumference (the length of the equator): 12800 km x π (≈ 3.14159) = approximately 40212 km
Therefore, the length of the equator is approximately 40212 kilometers. However, the accepted value for the Earth's radius from center to pole is 6371 km, which when calculated using the same formula provides a circumference of approximately 40030 km. The question assumes a simplified Earth radius, but using the more accurate radius yields a more precise equatorial length.