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The diameter of a miniture globe is fourty centimeters. The circumference of our earth is fourthousand miles (note: we're talking about scandinavian miles where one mile is equal to tenthousand meters). Calculate what volume scale that the miniture globe is produced by.

First off, sorry for the rough translation. Secondly, the answer should be 1:3*10^22 according to my book.

I've tried calculating the circumference of the miniature globe, and then comparing it to the circumference of the earth to get the length scale, and then of course I tried to cube the length scale so you get the volume scale, and I tried to calculate the volume by getting the radius . But I must've made mistakes or maybe I'm completely wrong because I can't get to the right answer. Sorry if this isn't descriptive, my keyboard on my computer is not working properly so I can't write all letters and numbers, so I hope this is enough for now.¨

Edit: I also want to state that I previously tried to calculate the earth's radius and then calculate the volume but I ended up with some weird numbers.

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The circumference of a circle is related to its diametre by $C=\pi D$. So the diametre of the Earth in metres is: $D_{\odot}=\frac{4\times 10^3\times 10\times 10^3}{\pi}=\frac{4\times 10^7}{\pi}$ metres. Now the diameter of the miniature is $D_m=0.4$ metre. Volume scales as the cube of the linear dimensions of similar solids, so the ratio of the volume of the Earth to the miniature is $$\left(\left[\frac{4\times10^7}{\pi}\right]/0.4\right)^3 \approx 3.2 \times 10^{22}$$

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  • $\begingroup$ Thank you for really showing me how to calculate the problem, it made me really understand what I did wrong and I could finally calculate the right answer thanks to your explanation. $\endgroup$
    – didnotcomeuptosomething
    Jan 3, 2015 at 20:08

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