Proportions

[lychee]

I have a question regarding this quote from a website:

"For the Brobdingnagians, their size can be deduced to be 12 times that of Gulliver, based on the following indirect statement:

“…a hailstone is near eighteen hundred times as large as one in Europe.” (Chapter V)" - https://jps.biomedcentral.com/articles/10.1007/s12576-018-00655-4

How were they able to deduce that the height of Brobdingnagians are 12 times Gulliver? Thanks!
P.S. I am not sure if this is the right category to post this on, but let me know.

 

[lev888]

I have a question regarding this quote from a website:

"For the Brobdingnagians, their size can be deduced to be 12 times that of Gulliver, based on the following indirect statement:


How were they able to deduce that the height of Brobdingnagians are 12 times Gulliver? Thanks!
P.S. I am not sure if this is the right category to post this on, but let me know.

If one sphere is 1800 times larger than another by volume, how are their radii related?

 

[HallsofIvy]

Actually the quote does NOT say that the height of the Brobdingnagians is 12 times that of Gulliver. It uses the word "size". Similarly, lev888 uses the phrase "larger than" when he means volume. I think both are ambiguous. Anyway, Lychee, the volume of a sphere is given by $\frac{4}{3}\pi r^3$. In fact, the calculation of any volume requires the cube of a length,