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A rectangular box without a lid is to be made from 27𝑚2 of cardboard. Find the maximum volume of such a box
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plz tell the answer if u know
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DGM
le 1 Juil 2021
This is a typical calculus 1 problem. You can do this as your course intends or approach it graphically to build your expectations/intuition. There are plenty of examples of solving this the intended way. The obvious thing to recognize is that for volume to be maximized for a fixed surface area, the bottom of the box must be square. This reduces the problem to a simple 1D maximization task. Express the volume as a function of area and width (or area and height). Treat the chosen dimension as the independent variable, and find the width (or height) at which the slope of V = 0. Back calculate to find the volume and remaining dimensions.
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