Take a piece of A4 (210mm x 297mm) paper and fold the sides up to form a tray so that the volume inside the tray is maximised.
What is the height of the tray when maximum volume is reached. Let the height = x
a quadratic equation, apparently
2007-01-10 02:23:38 · 5 answers · asked by desperado 1 in Science & Mathematics ➔ Mathematics
Volume = V = (210 - 2x) * (297 - 2x) * x = 62370x - 1014x^2 + 4x^3
dV/dx = 62370 - 2028x + 12x^2 = 0 when
x = (2028 +- sqrt(2028^2 - 4 * 12 * 62370)) / (2 * 12)
x = (2028 +- 1057.84) / 24 = 40.42 mm
2007-01-10 02:41:45 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Most people generally agree on some where between 7 and 9, but it really depends on how clearly the term 'fold' is. Do you mean that the paper doubles back on itself fully, or that when the paper is unfolded again it leaves a visible fold mark? If pushed, I'd say 8, regardless of paper size, though thinner papers like 'bank' paper can give you an extra fold.
2016-05-23 04:00:55 · answer #2 · answered by Elizabeth 4 · 0⤊ 0⤋
Volume = (210-2x)*(297-2x)*x
multiply through,... find the differential,... then locate the critical points...
one will be the max volume possible.
2007-01-10 02:30:04 · answer #3 · answered by beanie_boy_007 3 · 0⤊ 0⤋
x = 40 mm for v max
2007-01-10 02:42:39 · answer #4 · answered by runlolarun 4 · 0⤊ 0⤋
I dunno but I did as you said and made a little tray to carry Mr. GorgeousFluffpot's cup of tea to him, and the whole thing broke and I have tea all over the carpet now.
So I have had to dress up in my frilly maid's outfit and scrub the floor.
Satisfied?
2007-01-10 02:32:09 · answer #5 · answered by gorgeousfluffpot 5 · 0⤊ 1⤋