Could A Flea, A Rabbit Or Even A Man Squeeze Underneath It?

2 pi (r1-r2)=10

=> r1-r2=10/2*pi

=> r1-r2= 1.59

Radius of the earth (assuming it's perfectly spherical) is $\frac {40000} {2\pi} = 6366.19772...$

Radius of metal band with 10 metres added on is $\frac {40000.01} {2\pi} = 63661.9788...$

Subtract the second value from the first, then multiply by 1000 because the question asks for the answer in metres. The answer is therefore 1.6 (correct to 2 sig. fig).

To find how far the band has risen, we have to find out the change in the radius.

The circumference and the radius of a circle are proportinal. Therefore any change in the circumference will yeild a proportinal change in the radius.

We can use $C = 2\pi r$

We are given c1 = 40,000 and c2 = 40,000.01.

$\Delta C = c_2 - c_1 = 0.01 \quad and \quad \Delta C = 2\pi \Delta r$

$0.01 = 2\pi \Delta r \quad \rightarrow \quad \Delta r = {0.01 \over 2\pi} \quad \to \quad \Delta r \approx 0.00159 \text{ km} \approx 1.59 \text{ m}$

$$ This is one of the famous problems in Math. Let we generalize this problem. Let $L_1$ and $L_2$ , where $L_2>L_1$ , be the initial and final circumference, respectively. Let $d$ be the extension length. Therefore $$ $\begin{aligned} L_2-L1 &= 2\pi R_2 - 2\pi R_1\\ (L_1+d)-L_1 &= 2\pi (R_2 - R_1)\\ \Delta R &= \frac{d}{2\pi}\\ \end{aligned}$ $$ Thus, the 'levitation' of metal circle $\Delta R$ only depends on the extension length $d$ . Hence, for $d=10\,m$ we obtain $\Delta R = \frac{10}{2\pi}\approx \boxed{1.592}$ $$ $\text{\# }\mathbb{Q}.\mathbb{E}.\mathbb{D}.\text{\#}$

It will increase by 1.59m in all direction at all places! I know it's hard to believe but mathematics says so.

Answer = 10/2π = 1.6 m

SIMPLY put it its 2pi[R-r] is 10 is the concept.

The original radius is $r_{0} = \frac{C_{0}}{2\pi}$ . If we call the final radius $r$ we have $r = \frac{C}{2\pi}$ where $C = C_{0} + a$ and $a$ is the amount we add to the initial circumference. So the diference will be the value we are looking for:

$r - r_{0} = \frac{C - C_{0}}{2\pi} = \frac{a}{2\pi} = \frac{5}{\pi} \cong 1.6$

10/(2*3.14)=1.592

>> (40000.01/(2 3.1415926535) - 40000/(2 3.1415926535))*1000

1.5915494304863387

Use the formula Circumference = 2 × pi × Radius

Before: Original Circumference = 2 × pi × R After: Original Circumference + 10m = 2 × pi × (R + Gap)

Subtracting the two:

10m = 2 × pi × Gap

So, the Gap = 10m / (2 × pi) = 1.6m approximately

So a man could fit under it easily (though he might bump his head)

Note: Adding 10m to the circumference of ANY circle increases the radius by 10m / (2 × pi), no matter what the original circumference was.

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