A string around the Earth’s equator

Place a string around the Earth’s equator and pull it snug. Add a length of one meter to the string and push it away from the equator an equidistant amount. What is the largest animal, from the list below, that would now be able to walk under the string?

Flea Mouse Dachshund Calf Horse Elephant

Solution.

The length of the Earth’s equator is 40075000 m. The Earth’s equator is a great-circle.
The length of a circle’s circumference is defined as 2πr. We can find the radius of the Earth

r = L/2π, where L is the length of the Earth’s equator.

We substitute the values and solve for r

r = L/2π = 40075000/2π ≈ 6378134.34 m

We added one meter to the string. Hence, the length of the new string is 40075001 m. Now we can find the new radius

rnew = Lnew/2π

rnew = 40075001/2π ≈ 6378134.50 m.

Finally, we can calculate the difference between the new radius and the radius of the Earth

h = 6378134.50 – 6378134.34 = 0.16 m.

Here is an interesting fact: the height of the Miniature Dachshund is about 0.15 m. Hence, the Miniature Dachshund is the largest animal, from the list, that would now be able to walk under the string.

Source.