A very long piece of string indeed!

Algebra Level 3

Imagine a hugely long piece of string. One that completely goes around the equator to form a circle.

The string is then lengthened by just 1 metre and forms another larger concentric circle. How far away from the equator in centimetres is the new circle of string.

Assumption: The earth is a sphere of radius approximately 6400 km.


The answer is 15.9.

Chaz Dodd by Chaz Dodd , 45, Australia

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Let the radius of the Earth be R R cm and the radius of the new circle be R 1 R_1 cm. Then the distance the new circle is away from the equator is d = R 1 − R d=R_1-R and

2 π R 1 = 2 π R + 100 R 1 = R + 100 2 π R 1 − R = 100 2 π d ≈ 15.9 \begin{aligned} 2\pi R_1&= 2\pi R+100 \\ R_1&= R+ \frac {100}{2\pi} \\ R_1-R &= \frac {100}{2\pi} \\ d & \approx \boxed{15.9}\end{aligned}

Note that d d is independent of R R .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Also dR/dC= 1/(2pi) so a change in C of 1 gives a change in R of 0.159 approx therefore 15.9 cm Which would as you said be the same distance if the sphere was a grapefruit.

Chaz Dodd - 3 years, 6 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...