Question

NEED SOMEONE WITH BIG BRAINS

Imagine we have a piece of string 25,000 miles long, just long enough to exactly circle the globe at the equator. We take the string and fit it snugly around the equator, over oceans, deserts and jungles. When we have completed our task, we find that the string is just one yard too long. To overcome the error, we decide to tie the ends together and to distribute the extra 36 inches evenly over the entire 25,000 miles, figuring that it will never be noticed. How far do you think the string will stand off from the ground at each point, merely by virtue of the fact that it is 36 inches (3 feet) too long? Explain your answer.

Answer 1

Answer: just an extra one foot

Explanation:

Given that the length of the piece of string = 25,000 miles

Since the string is long enough to exactly circle the globe at the equator over oceans, deserts and jungles. We can say that the string could completely circle a sphere

Assuming that the earth is a perfect sphere.

The circumference of the circle = 25,000 mile.

But note that the circumference of a circle is directly proportional to the radius. If you double the radius, the circumference will also be doubled. Half the circumference, half the radius. Increase the circumference by 30%, radius will also be increased by 30% and so on.

In this question, the radius is being increased by 3 feet, so we need to know that as a fraction of the original radius.

Circumference = 2πr

Let's also convert miles to feet

25000 × 5280 = 2(3.143)r

r = 132 × 10^6/2π

r = 21008452.5 feet

3 feet - that's how far off the ground we're lifting the string out of 21008452.5 feet is close to one part in 25000 miles. The string was 132000000 feet long to start with, so we need just an extra 1 foot.