3 ms·
I thought for a second it wouldn't work like that, but it does! You are increasing the length of one of the sides by 33%, but decreasing by 25% to get to rough
by romwell 6y ago
I thought for a second it wouldn't work like that, but it does!
You are increasing the length of one of the sides by 33%, but decreasing by 25% to get to roughly-a-cube. The product of ratios is 3/4 * 5/4 = 15/16, or about 6% underestimate.
Of course, this is already pretty close, and the third side being 107 and not 100 corrects for that.
In the end, that's because (1-x)(1+x) = 1-x^2, so if if the amount we're doing this with is under 20%, our error is under %4 (i.e. pretty good for rough estimates).