Open Box: Maximising Volume
- Mathematics
- Class 12
- 3D model
- English · Hindi
Open Box: Maximising Volume: a 3D model for Class 12 Mathematics, covering Cut a square of side x from each corner of a square sheet of side a and fold up the flaps to make an open box., The base is (a − 2x) by (a − 2x) and the height is x, so the volume is V(x) = x(a − 2x)², for 0 < x < a/2., A tiny cut gives a wide, shallow tray and a big cut a tall, narrow box; in between, the volume is greatest., At the greatest volume the tangent to the V(x) curve is level: the derivative dV/dx is zero there., dV/dx = (a − 2x)(a − 6x) = 0 gives x = a/6; V″(a/6) < 0, so the cut x = a/6 gives the maximum..
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Also called
open box problem · maximum volume · maxima and minima · optimisation · cut squares from the corners · V = x(a − 2x)² · dV/dx = 0 · first derivative test · second derivative test · local maximum · least surface area of a can · cylinder of maximum volume · उच्चिष्ठ और निम्निष्ठ · अवकलज के अनुप्रयोग · आयतन
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About this model
A GLB file of about 495 KB, shown in Lably's 3D viewer and, on a phone, placed in your room with AR. Credit: Model, science and animation: Lably (built procedurally with three.js; no downloaded meshes). | CC BY 4.0. Original geometry and animation made for Lably.
