Math, Math help

Question

The Greek mathematician Eratosthenes (ca 276 bce − 196 bce) estimated that the Earth's circumference measured 252,000 stadia. There was no standard for the value of a stadio, but it is estimated that in Eratosthenes' calculations a stadio was equivalent to 157.7m. We know today that the circumference of the Earth at the equator is 40,075.017 km. What was Eratosthenes’s absolute error? What was his relative error?

Answer 1

40,075,070 m = 40,075.070 km

-39,740,400 m = 39,740.400 m

= 334,670 meter error

= 334.67 kilometer error

1 -39,740,00/40,075,070 =100- 99.1638941% =about 0.00.84% error

earth's radius as a sphere = about 6367 km give or take 10 or so km

Circumference = pid = 2rpi = 2(6367)(3.14159) = 40,005 km

Circumference around the equator is an estimated 40,075 km

Circumference around the poles is an estimated 40,008 km