I'm having trouble with this and am unsure what I'm doing wrong. Let's use Earth as an example.

Earth has a mass of 5,972,168,000,000,000,000,000,000 (5.97E+27) kg and a density of 5513.4 kg/m3 or 5.5134 g/cm3.

Volume = mass / density.

The calculation gives me a result of 1,086,109,090,909,090,000,000,000.00 (1.09E+24) m3. However, the Earth's volume is 1,083,210,000,000,000.00 m3. That's a 1 billion times difference.

Is there a discreprancy with the units this question advised to always use kg and m2?

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    $\begingroup$ Earth's volume from wikipedia is $1.0832 \times10^{12} $ km, not $1.0832 \times10^{12} $ m. Correct this error and you'll see you calculated approximately the right answer the first time. $\endgroup$
    – Connor Garcia
    Jun 17, 2023 at 20:13
  • $\begingroup$ I cannot correct the volume as this is the value I'm trying to calculate from the forumla. I can only change the mass or density. I can however fix my reference to know what the value should be, so thank you for pointing that out. $\endgroup$ Jun 17, 2023 at 20:53
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    $\begingroup$ Your Earth mass is off by a factor 1000, that's jupiter mass. The mass of earth is is $6\cdot 10^{24}$kg. $\endgroup$ Jun 18, 2023 at 0:29

1 Answer 1


Your Earth mass is off by a factor of 1000

As @planetmaker has pointed out, the mass of the earth is $6$$⋅$$10^{24}$ kg, instead of $6$$⋅$$10^{27}$.

Second, $km^{3}$ and $m^{3}$ are different things. $km^{3}$ is off $m^{3}$ by a factor of 1 billion ($1km^{3}$=$10^9m^{3}$).

Correct your calculations using these factors. If calculations are correct, you should obtain $1.08321 × 10^{21}$$m^3$ as your correct answer.


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