+0

Fun challenge question.

+3
508
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+106885

Here is a fun question for some people.

If it is very easy for you then please do not answer.

It is intended to be a interesting challenge question.

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Assume the Earth is a perfect sphere.

A peice of string is wrapped around the equator to make a snug fit.

Now another string exactly one metre longer than the first one is wrapped around the earth so that the 2 peices of string form 2 concentric circles.

How far off the surface of Eath is the second peices of string?

Nov 4, 2019

#1
+2551
+5

$$2{\pi}r=C$$

That is the formula for circumference.

Now to find how far off, we find the difference between the two radii when the concentric circles are formed.

We make a system of equations

$$2{\pi}x=C$$

$$2{\pi}y=(C+1)$$

We have to evaluate $$|y-x|$$

Substituting: $$2{\pi}y-1=2{\pi}x$$

Simplifying: $$1=2{\pi}y-2{\pi}x$$

Solving: $$\frac{1}{2{\pi}}=y-x$$

Solving for $$|y-x|$$,

$$\boxed{\frac{1}{2{\pi}}}$$

That was my attempt

Nov 4, 2019

#1
+2551
+5

$$2{\pi}r=C$$

That is the formula for circumference.

Now to find how far off, we find the difference between the two radii when the concentric circles are formed.

We make a system of equations

$$2{\pi}x=C$$

$$2{\pi}y=(C+1)$$

We have to evaluate $$|y-x|$$

Substituting: $$2{\pi}y-1=2{\pi}x$$

Simplifying: $$1=2{\pi}y-2{\pi}x$$

Solving: $$\frac{1}{2{\pi}}=y-x$$

Solving for $$|y-x|$$,

$$\boxed{\frac{1}{2{\pi}}}$$

That was my attempt

CalculatorUser Nov 4, 2019
#2
+106515
+3

Correct, CU  !!!

Good job  !!!

CPhill  Nov 4, 2019
#3
+106885
+2

Great work CalculatorUser!

You maths is excellent,

Just for a slightly different presentation I could say:

$$C=2\pi r\\ \frac{C}{2\pi}=r\\ \frac{C+1}{2\pi}=\frac{C}{2\pi}+\frac{1}{2\pi}=r+\frac{1}{2\pi}$$

So if the circumference is increased by 1 unit, the radius is increased by  $$\frac{1}{2\pi}\;units$$

So if the circumference is increased by 1 metre, the radius is increased by $$\frac{1}{2\pi}\;metre$$

And this equals an approximate radius increas of  0.159 metres or approx  16cm

This distance between the 2 concentric circles will always be the same.

It does not matter how big or small the original circle is.

Melody  Nov 4, 2019
edited by Melody  Nov 4, 2019