Quote:
Originally Posted by potatodave
no, if volume is doubled, then mass is doubled. If the dimensions, however are doubled, then mass is multiplied by 8.
If mass or volume changes by any factor and it is assumed that all dimensions increase equally to accommodate that factor, then each of the three dimensions will change by the cubic root of that factor. If the dimensions change equally by any factor, then the mass and volume change by that factor cubed.
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It gets worse. Whoever wrote that note Hawkeye quoted messed up the arithmetic.
Taking the 73 gallons (wherever they got that from) does give 584 pounds. But water has a density of 62.5 lbs/ft^3 (or 1000 kg/m^3), so 584 lbs. only has a volume of 9.34 cubic feet. You can get the diameter of a sphere by dividing its volume by about 0.524, and then taking the cube root of that result. [I'll be happy to supply the derivation if anyone really wants it...] So you only get a diameter of about 2.6 feet,
not 24 feet!
(C'mon, there are water towers with diameters of 24 feet -- a sphere of water that big would weigh over 200 tons! Another check:
you're mostly water! If you and two friends, weighing around 450-600 pounds total, huddled down to form a rough sphere, how big across would that be? Closer to 3 feet across, or 24 feet?)